Volume-11 , Issue-6 , Dec 2024, ISSN 2348-4519 (Online)

• Open Access   Article

  Progression of Optimizational Principles in Portfolio Analysis through Isolated Entropic Models

  Poonam Kumari

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.1-8, Dec-2024

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  Abstract
  Even if there is a vast array of parametric and non-parametric information models, predictability still emerges to expand further parametric models to strengthen plasticity in the structure under study. Additionally, there looks to be a well-built association sandwiched between information entropy and the theory of “Portfolio Analysis”. Moreover, innumerable methodologies of risk assessment, comprising entropy technique, divergence procedure, unified approach, etc. are accessible within the existing corpus of portfolio analysis literature. The present paper is a step towards making progress on some well-known optimizational principles by using new discrete entropic models and then showing how they can be used in portfolio analysis. In addition, the entrenched principle has been elucidated through the support of a well-managed numerical example.

  Key-Words / Index Term
  Portfolio analysis, Modern portfolio theory, Entropy, Variance, Covariance matrix, Uncertainty

  References
  [1] H. M. Markowitz, “Portfolio selection,” The Journal of Finance, Vol.7, Issue.1, pp.77-91, 1952.
  [2] H. M. Markowitz, “Portfolio Selection: Efficient Diversification of Investments,” John Wiley and Sons, 1959.
  [3] C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, Vol.27, Issue.3, pp.379–423, 1948.
  [4] K. Bisht and A. Kumar, “A portfolio construction model based on sector analysis using Dempster-Shafer evidence theory and Granger causal network: An application to National stock exchange of India,” Expert Systems with Applications, Vol.215, 119434, 2023.
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  [8] R. Soyer and K. Tanyeri, “Bayesian portfolio selection with multi-variate random variance models,” European Journal of Operational Research, Vol.171, Issue.3, pp.977–990, 2006.
  [9] A. K. Bera, and S. Y. Park, “Optimal Portfolio Diversification Using the Maximum Entropy Principle,” Econometric Reviews, Vol. 27, Issue.4–6, pp.484–512, 2008.
  [10] J. Xu, X. Zhou, and D. D. Wu, “Portfolio selection using ? mean and hybrid entropy,” Annals of Operations Research, Vol.185, Issue.1, pp.213–229, 2009.
  [11] I. Usta and Y. M Kantar, “Mean-Variance-Skewness-Entropy Measures: A Multi-Objective Approach for Portfolio Selection,” Entropy, Vol.13, Issue.1, pp.117–133, 2011.
  [12] N. Lassance and F. Vrins, “Minimum Rényi entropy portfolios,” Annals of Operations Research, Vol.299 (1–2), pp.23–46, 2019.
  [13] H. Rau-Bredow, “Bigger Is Not Always Safer: A Critical Analysis of the Subadditivity Assumption for Coherent Risk Measures,” Risks, Vol.7, Issue.3 (91), 2019.
  [14] L. MacLean, L. Yu, and Y. Zhao, “A Generalized Entropy Approach to Portfolio Selection under a Hidden Markov Model,” Journal of Risk and Financial Management, Vol.15, Issue.8 (337), 2022.
  [15] P. J. Mercurio, Y. Wu, and H. Xie, “An Entropy-Based Approach to Portfolio Optimization,” Entropy, Vol.22, Issue.3 (332), 2020.
  [16] Y. Lu, M. Wang, W. Wu, Q. Zhang, Y. Han, T. Kausar, S. Chen, M. Liu and B. Wang, “Entropy-Based Pattern Learning Based on Singular Spectrum Analysis Components for Assessment of Physiological Signals,” Complexity, Article ID 4625218, 2020.
  [17] S. Li, J. Peng, B. Zhang, and D. Ralescu, D, “Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns,” International Journal of Management and Fuzzy Systems, Vol.7, Issue.3 (47), 2021.
  [18] J. Zhang and J. Shi, “Asymptotic normality for plug-in estimators of generalized Shannon`s entropy,” Entropy, Vol.24, Issue5 (683), 2022.
  [19] P. Saraiva, “On Shannon entropy and its applications,” Kuwait Journal of Science, Vol. 50, Issue 3, pp.194-199, 2023.
  [20] Vikramjit Singh, Sunil Kumar Sharma, Om Parkash, Retneer Sharma and Shivam Bhardwaj, “A newfangled isolated entropic measure in probability spaces and its applications to queueing theory,” AIMS Mathematics, Vol.9, Issue.10, pp.27293-27307, 2024.
  [21] M. A. A. Elgawad, H. M. Barakat, S. Xiong and S. A. Alyami, “Information measures for generalized order statistics and their concomitants under general framework from huang-kotz fgm bivariate distribution,” Entropy, Vol.23, Issue.3 (335), pp.1-17, 2021.
  [22] O. Parkash, V. Singh, and R. Sharma, “A new discrete information model and its applications for the study of contingency tables,” Journal of Discrete Mathematical Sciences and Cryptography, Vol.25, Issue.3, pp.785–792, 2022.
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  [25] A. Renyi, “On measures of entropy and information,” Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol.1, pp.547-561, 1961.

  Citation
  Poonam Kumari, "Progression of Optimizational Principles in Portfolio Analysis through Isolated Entropic Models," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.1-8, 2024

• Open Access   Article

  Reliability, Maintainability and Sensitivity Analysis of Poultry Feed Processing Plant

  Nazir Isma’il Ibrahim, Mansur Hassan, Mansur Nuhu Alhassan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.9-16, Dec-2024

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  Abstract
  This research examines the availability, maintainability and sensitivity of a poultry feed processing plant to optimize operational performance. Availability is assessed using Mean Time between Failures (MTBF) and Mean Time to Repair (MTTR), revealing a gradual decline over time due to equipment failures. Maintainability analysis focuses on repair efficiency, highlighting the plant’s ability to quickly restore machinery after breakdowns. Sensitivity Analysis identifies preventive maintenance frequency and spare parts availability as key factors affecting system performance. The findings provide means to reduce downtime and improve operational reliability in poultry feed processing. Graphical analysis of availability shows a consistent decline over time across all equipment. Maintainability analysis reveals that despite a high initial recovery rate, minor deviations in repair times can significantly impact overall operational uptime.

  Key-Words / Index Term
  Poultry, Processing Plant, Availability, Maintainability, Sensitivity, feed

  References
  [1] F. Corvaro, G. Giacchetta, B. Marchetti, M. Recanati. “Reliability, availability, maintainability (RAM) study, on reciprocating compressors API 618”. Journal of Petroleum Management, Vol.3, No.2, pp.266–272, 2017.
  [2] H. Garg. “Reliability, availability and maintainability analysis of industrial system using PSO and fuzzy methodology”, MAPAN-Journal of Metrology Society of India, Vol.29, No.2, pp.115–129, 2014.
  [3] N. Kumar, P. C. “Tewari, A review on the reliability, availability and maintainability (RAM) approaches in conceptual progress design”, In Proceedings of the International Conference on Industrial Engineering and Operations Management, Bandung, Indonesia, pp.6–8, 2018.
  [4] A. Lado, V. V. Singh, “Cost assessment of complex repairable systems in series configuration using Gumbel Hougaard family copula”, International Journal of Quality and Reliability Management, Vol.36, No.10, pp.1683–1698, 2019.
  [5] R. Malhotra, T. Dureja, A. Goyal, “Reliability analysis a two-unit cold redundant system working in a pharmaceutical agency with preventive maintenance”, Journal of Physics, Vol.18, No.12, pp.1–10, 2021.
  [6] M. Saini, A. Kumar, V. G. Shankar, “A study of microprocessor systems using RAMD approach”, Life Cycle Reliability and Safety Engineering, Vol.20, No.11, pp.1-6, 2020.
  [7] A. Sanusi, I. Yusuf, “Reliability, availability, maintainability, and dependability (RAMD) analysis of computer based test (CBT) network system”, RT&A, Vol.16, No.3, pp.99–114, 2021.
  [8] V. V. Singh, H. I. Ayagi, “Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel Hougaard family copula”, International Journal of Mathematics in Operational Research, Vol.12, No.2, pp.273–292, 2018.
  [9] P. Tsarouhas, “Reliability, availability and maintainability (RAM) analysis for wine packaging production line”,. International Journal of Quality & Reliability Management, Vol.35, No.3, pp.821–842, 2018.
  [11] K. Velmurugan, P. Venkumar, R. Sudhakarapandian, “Reliability availability maintainability analysis in forming industry”, International Journal of Engineering and Advanced Technology, Vol.91, No.4, pp.822–828, 2019.
  [12] I. Yusuf, M. Anas, I. Y. Saminu, “Reliability and performance analysis of a series–parallel system using Gumbel–Hougaard family copula”. Journal of Computation and Cognitive Engineering, Vol.1, No.1, pp.1–10, 2021.
  [13] H. Garg, “Reliability and industrial engineering problems: theory and applications”, Recent Advances in Computer Science and Communications, Vol.15, No.4, pp.480–483, 2022.
  [14] Y. He, C. Gu , X. Han, J. Cui, Z. Chen, “Mission reliability modelling for multi-station manufacturing system based on quality state task network”, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, Vol.231, No.2, pp.701–715, 2017.
  [15] M. Kamal, U. Modibbo, M. AlArjani, “Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability”, Complex & Intelligent Systems, Vol.7, No.3, pp.1045–1059, 2021.

  Citation
  Nazir Isma’il Ibrahim, Mansur Hassan, Mansur Nuhu Alhassan, "Reliability, Maintainability and Sensitivity Analysis of Poultry Feed Processing Plant," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.9-16, 2024

• Open Access   Article

  Comparative Analysis of Registered Cyber-Crimes among Rajasthan and Its Neighbouring States

  Deepak Kumar Parewa, Deepa Mordia

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.17-22, Dec-2024

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  Abstract
  This research paper examines the trends and comparative analysis of registered cyber-crimes across Rajasthan and its neighbouring states—Gujarat, Haryana, Madhya Pradesh, Punjab, and Uttar Pradesh—from 2012 to 2021. Rajasthan, a prominent state in India, has witnessed rapid digital growth alongside its traditional socio-economic development. However, this growth has also brought an increase in cyber-crimes. The study utilizes secondary data analysis to explore the annual variations in both the absolute numbers and percentages of cyber-crimes reported. Descriptive statistics, ANOVA, and Tukey`s HSD tests are employed to analyze the differences in cyber-crime prevalence among the states. Findings reveal significant disparities in cyber-crime rates, with Rajasthan consistently showing a higher prevalence compared to most neighbouring states. Uttar Pradesh emerges as particularly vulnerable, reporting the highest percentage of cyber-crimes. These results underscore the need for tailored regional strategies to enhance cyber security measures and mitigate the growing threat of cyber-crimes across the studied states.

  Key-Words / Index Term
  Cyber Crimes, Rajasthan and Neighbouring States, Comparative Analysis, Cyber Security

  References
  [1] Kshetri, N., The Global Cybercrime Industry: Economic, Institutional and Strategic Perspectives, Springer, 2010.
  [2] Singh, A., “Cyber Crime in the Digital Age: Challenges and Solutions,” Indian Journal of Criminology, Vol.41, Issue.1, pp.15-29, 2013.
  [3] Gupta, M., & Bajaj, S., “Cyber Crime and Security: A Study of Select States in India,” Journal of Cybersecurity Studies, Vol.4, Issue.2, pp.75-89, 2017.
  [4] Ch, R., Gadekallu, T. R., Abidi, M. H., & Al-Ahmari, A., “Computational system to classify cyber-crime offenses using machine learning,” Sustainability, Vol.12, Issue.10, pp.4087, 2020.
  [5] National Crime Records Bureau (NCRB), Crime in India 2020: Statistics, Ministry of Home Affairs, Government of India, 2021.
  [6] Horan, C., & Saiedian, H., “Cybercrime investigation: Landscape, challenges, and future research directions,” Journal of Cybersecurity and Privacy, Vol.1, Issue.4, pp.580-596, 2021.
  [7] Khan, S., Saleh, T., Dorasamy, M., Khan, N., Tan Swee Leng, O., & Gale Vergara, R., “A systematic literature review on cybercrime legislation,” F1000Research, Vol.11, pp.971, 2022.
  [8] Shah, N., Rajadhyaskha, A., & Hasan, N., “Overload, Creep, Excess--An Internet from India,” In the Proceedings of the 2022 International Conference on Internet Studies, India, pp.542-545, 2022.
  [9] Syahril, M. A. F., “Cyber Crime in terms of the Human Rights Perspective,” International Journal of Multicultural and Multireligious Understanding, Vol.10, Issue.5, pp.119-130, 2023.
  [10] Whelan, C., Bright, D., & Martin, J., “Reconceptualising organised (cyber) crime: The case of ransomware,” Journal of Criminology, Vol.57, Issue.1, pp.45-61, 2024.

  Citation
  Deepak Kumar Parewa, Deepa Mordia, "Comparative Analysis of Registered Cyber-Crimes among Rajasthan and Its Neighbouring States," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.17-22, 2024

• Open Access   Article

  An Efficient Numerical Scheme for the Solution of Integer-Order Delays Differential Equations

  Ibrahim M.D., M.S. Adamu, Isah Abdullahi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.23-31, Dec-2024

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  Abstract
  This study presents the MNIM approach, which integrates the El-Kalla polynomial with a new iterative method. The linear components of delay differential equations (DDEs) are first addressed using the new iterative method, followed by a secondary iterative process to manage the complexities introduced by nonlinear terms, as detailed in Section 2.3. Essential definitions and concepts related to DDEs, the iterative methodology, and the El-Kalla polynomial are also discussed. The effectiveness and reliability of MNIM are demonstrated through three notable test cases, with absolute errors evaluated both graphically and numerically for different values of the time variable xxx. The findings emphasize MNIM`s capability to produce highly accurate approximations that closely match exact solutions with minimal error. This highlights MNIM`s potential as a powerful and efficient tool for solving nonlinear DDEs. Additionally, the study lays the groundwork for future research, showcasing the method`s potential in addressing complex problems across various scientific and engineering fields where nonlinear DDEs play a key role in modeling.

  Key-Words / Index Term
  Delay differential equations; Fractional delay differential equations; El-kalla polynomials; Adomian polynomials

  References
  [1] Jhinga, V., & Daftardar-Gejji, V., "An innovative predictor-corrector technique for nonlinear fractional delay differential equations," 2019.
  [2] Srivastava, V., "Approximate Analytical Solution of Linear and Nonlinear Fractional Delay Differential Equations using Variational Iteration Method," Open Science Journal, vol. 5, no. 4, pp. 1–11, 2020.
  [3] Du, M. J., "A Specific Method for Solving Fractional Delay Differential Equation via Fraction Taylor’s Series," Mathematical Problems in Engineering, vol. 2022, pp. 1–6, 2022.
  [4] El-Kalla, I. L., Elgaber, K. M. A., Elmahdy, A. R., & Sayed, A. Y., "Solution of a Nonlinear Delay Differential Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomial," American Journal of Computational Mathematics, vol. 9, no. 4, pp. 221–233, 2019.
  [5] Avc?, D., "Numerical solutions for fractional delay differential equations using Caputo fractional derivatives," 2022.
  [6] Diethelm, K., Ford, N. J., & Freed, A. D., "Detailed error analysis for a fractional Adams method," Numerical Algorithms, vol. 36, pp. 31–52, 2004.
  [7] Diethelm, K., Ford, N. J., Freed, A. D., & Luchko, Y., "Algorithms for the fractional calculus: A selection of numerical methods," Computers and Mathematics with Applications, vol. 48, no. 10, pp. 1047–1061, 2002.
  [8] Bhalekar, S., & Daftardar-Gejji, V., "A fractional Adams method for initial value problems with delay terms," Journal of Computational and Applied Mathematics, vol. 235, no. 12, pp. 3442–3450, 2011.
  [9] Daftardar-Gejji, V., Jafari, H., & Bhalekar, S., "Numerical Predictor-Corrector Method for Solving Fractional Delay Differential Equations," Journal of Computational Analysis and Applications, vol. 16, pp. 1–11, 2014.
  [10] Daftardar-Gejji, V., & Jafari, H., "An iterative method for solving nonlinear functional equations," Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 753–763, 2006.
  [11] Bhalekar, S., & Daftardar-Gejji, V., "Solving fractional boundary value problems using a new iterative method," Computers and Mathematics with Applications, vol. 59, no. 5, pp. 1801–1809, 2010.
  [12] Daftardar-Gejji, V., & Kumar, R., "Error analysis for numerical methods in fractional delay differential equations," Applied Numerical Mathematics, vol. 126, pp. 60–72, 2018.
  [13] Daftardar-Gejji, V., Bhalekar, S., & Kumar, R., "Improved Predictor-Corrector Method for Fractional Delay Differential Equations," Computational Mathematics and Modeling, vol. 26, no. 3, pp. 345–360, 2015.
  [14] Kumar, R., & Methi, S., "Application of Banach Contraction Principle to Fractional Delay Differential Equations," Mathematical Problems in Engineering, vol. 2021, pp. 1–10, 2021.
  [15] Daftardar-Gejji, V., & Bhalekar, S., "Banach Contraction Method for Fractional Differential Equations," 2009.

  Citation
  Ibrahim M.D., M.S. Adamu, Isah Abdullahi, "An Efficient Numerical Scheme for the Solution of Integer-Order Delays Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.23-31, 2024

• Open Access   Article

  Electromagnetic Radiation through an Ideal Gas and its Analytic Solution Using Fourier Transform and Greens Function

  Maulik S Joshi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.32-38, Dec-2024

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  Abstract
  This paper explores the significance of solving physical problems in an infinite domain using mathematical techniques. While physical problems are never truly infinite, discussing them in an infinite domain allows us to weaken the influence of boundaries and obtain solutions that provide valuable insights. Among various analytic approaches to solve partial differential equations, explicit solutions hold particular importance as they offer a clearer understanding of the problem.

  Key-Words / Index Term
  Fourier Transform, Wave operator, Dirac delta function, Green function, Green’s formula, Electromagnetic radiation

  References
  [1] Haberman R., “Elementary Applied Partial Differential Equations with Fourier series and Boundary value problems” - Prentice Hall Inc.- pp. 390-416,1983.
  [2] Pinsky M.A., “Partial Differential Equations and Boundary-Value Problems with Applications”- McGraw-Hill-1998, pp. 277-343, 1998.
  [3] Muhlenbruch T. , Raji W. “On the Theory of Mass Wave Forms”, First edition Springer Cham. pp 1-250,2020.
  [4] Roach G F, Green’s functions- “Introductory Theory with Applications”- Van Nostrand Reinhold Company. pp.1-8,140-276,1967.
  [5] Relay K. G. , Hobson M P., Bence S J.- “Mathematical methods for physics and engineering” Cambridge University Press- pp.1-120, -2006.
  [6] Bracewell R N. (2000). The Fourier Transform and its applications McGraw-Hill Education , pp.1-6, 2000.

  Citation
  Maulik S Joshi, "Electromagnetic Radiation through an Ideal Gas and its Analytic Solution Using Fourier Transform and Greens Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.32-38, 2024

• Open Access   Article

  Hybrid of Semi-Analytical Methods for the Solution of Fractional Fredholm Integro-Differential Equations

  M.Z. Olakanse, J.O. Okai, Micheal Cornelius

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.39-46, Dec-2024

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  This seminar introduces a hybrid approach combining the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) to enhance the performance of ADM (Ansari & Ahmad, 2023) in solving fractional integro-differential equations. The primary objective of the research is to eliminate the use of Lagrange’s multiplier in ADM and the Adomian polynomial in VIM. A new scheme is proposed, offering series solutions for both integer and non-integer orders. The proposed method demonstrates superiority over its counterparts, and several examples are presented to validate its effectiveness.

  Key-Words / Index Term
  Fractional integro-differential equation, Adomian decomposition method, Variational Iteration method

  References
  [1] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, 1999.
  [2] Y. Song, "Numerical solutions of fractional differential equations using modified variational iteration method," Mathematical Problems in Engineering, vol. 2016, pp. 1–12, 2016.
  [3] M. A. F. Araghi, S. G. Dogaheh, and Z. Sayadi, "The modified variational iteration method for solving linear and nonlinear ordinary differential equations," Australian Journal of Basic and Applied Sciences, vol. 5, no. 10, pp. 406–416, 2011.
  [4] T. A. Abassy, "Modified variational iteration method (non-homogeneous initial value problem)," Mathematical and Computer Modelling, vol. 55, no. 3–4, pp. 1222–1232, 2012.
  [5] A. Ansari and N. Ahmad, "Numerical accuracy of Fredholm linear integro-differential equations by using Adomian decomposition method, modified Adomian decomposition method, and variational iteration method," Journal of Science and Arts, vol. 23, no. 3, pp. 625–638, 2023.
  [6] A. M. Wazwaz, A First Course in Integral Equations. World Scientific Publishing Company, 2007.
  [7] T. Oyedepo, C. Yemisi, A. Ajimoti, and O. Lukman, "Computational algorithm for fractional Fredholm integro-differential equations," Kathmandu University Journal of Science, Engineering and Technology, vol. 17, no. 1, pp. 1–6, 2023.
  [8] K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, 2010.
  [9] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, 2006

  Citation
  M.Z. Olakanse, J.O. Okai, Micheal Cornelius, "Hybrid of Semi-Analytical Methods for the Solution of Fractional Fredholm Integro-Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.39-46, 2024

• Open Access   Article

  Mathematical Analysis of Fractional Burgers` Fluid Model of Magnetohydrodynamic Blood Flow through Bifurcated Arteries

  Isah Abdullahi, M.Y Adamu, A. M Kwami, Munira Salisu

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.47-59, Dec-2024

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  Abstract
  The study analyzes electro-magnetohydrodynamic (EMHD) flow in bifurcated arteries using a non-Newtonian Burgers` fluid model with an Atangana-Baleanu fractional derivative. The focus is on how magnetic fields, electric fields, and thermal properties affect blood flow, especially for enhancing tumor treatment via controlled heat transfer. The study formulates the nonlinear partial differential equations (momentum, energy, and concentration) and solved analytically using the combine Laplace transforms and the Homotopy Perturbation Method (HPM). The results show that parameters such as magnetic field strength, Burgers` parameter, fractional parameters, Eckert number, and Joule heating influence blood flow velocity, temperature, and concentration within the arteries. Specifically, stronger magnetic fields and higher Burgers` parameters reduce blood velocity, while thermal factors like Eckert number and Joule heating increase temperature. These insights are valuable for biomedical applications such as targeted drug delivery, heat management, and tumor therapy.

  Key-Words / Index Term
  Bifurcated artery, Burgers’ fluid model, Atangana-Baleanu Fractional time derivative, Magnetic field, Thermal radiation, Heat transfer

  References
  [1] T. Hayat, M. Qasim, and Z. Abbas, "Peristaltic motion of a Burger`s fluid in a porous medium with heat and mass transfer," Int. J. Heat Mass Transfer, vol. 54, no. 19-20, pp. 4305-4312, 2011.
  [2] M. Khan and I. Shahzadi, "Numerical study of MHD flow and heat transfer of Burgers’ fluid over a stretching sheet," Appl. Math. Comput., vol. 268, pp. 459-469, 2015.
  [3] T. Hayat, T. Muhammad, and M. Farooq, "Magnetohydrodynamic oscillatory flow of Burgers’ fluid in a porous medium with thermal radiation," J. Mol. Liquids, vol. 220, pp. 477-484, 2016.
  [4] D. G. Yakubu, M. G. Abdulhameed, G. T. Adamu, R. Roslan, A. Issakhov, and M. Rahini-Gorji Bakouri, "Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative, magnetic field and thermal radiation effects," J. Process Mech. Eng., 2021.
  [5] A. Atangana and D. Baleanu, "New fractional derivative with non-local and non-singular kernel: Theory and application to heat transfer model," Thermal Sci., vol. 21, no. 2, pp. 761-766, 2016.
  [6] J. A. Smith and B. R. Johnson, "Control of fractional order systems using Atangana-Baleanu fractional derivatives," IEEE Trans. Control Syst., vol. 45, no. 3, pp. 789-802, 2022.
  [7] X. Chen and Y. Wang, "Analytical solutions of Atangana-Baleanu fractional differential equations in viscoelasticity," J. Mater. Sci., vol. 35, no. 7, pp. 1585-1597, 2023.
  [8] I. A. Mirza, M. Abdulhameed, and S. Shafie, "Magnetohydrodynamic approach of non-Newtonian blood flow with magnetic particles in stenosed artery," Appl. Math. Mech., vol. 38, no. 3, pp. 379-392, 2017.
  [9] D. Kumar, B. Satyanarayana, K. Rajesh, D. Narendra, and K. Sanjeev, "Application of heat source and chemical reaction in magnetohydrodynamic blood flow through permeable bifurcated arteries with inclined magnetic field in tumor treatments," J. Result Appl. Math., vol. 10, pp. 1-13, 2021.
  [10] A. Isah, A. Musa, D. G. Yakubu, G. T. Adamu, A. Mohammed, A. Baba, S. Kadas, and A. Mahmood, "The impact of heat source and chemical reaction on MHD blood flow through permeable bifurcated arteries with tilted magnetic field in tumor treatments," Comput. Methods Biomech. Biomed. Eng., 2023.
  [11] A. Rauf and Y. Mahsud, "Electro-magneto-hydrodynamic flows of Burger fluids in cylindrical domains with time exponential memory," J. Appl. Comput. Mech., vol. 5, no. 4, pp. 577-591, 2019.
  [12] M. Abdulhameed, G. T. Adamu, and D. G. Yakubu, "Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers’ fluid through micro-channel," J. Process Mech. Eng., 2021.
  [13] J. Escandon, E. Jimenez, O. Hernandez, O. Bautista, and F. Mendez, "Transient electroosmotic flow of Maxwell fluids in a slit microchannel with asymmetric zeta potentials," Eur. J. Mech. B/Fluids, vol. 53, pp. 180-189, 2015.
  [14] J. H. He, "Homotopy perturbation method," Comput. Math. Appl., vol. 37, no. 5, pp. 89-99, 1999.
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  Citation
  Isah Abdullahi, M.Y Adamu, A. M Kwami, Munira Salisu, "Mathematical Analysis of Fractional Burgers` Fluid Model of Magnetohydrodynamic Blood Flow through Bifurcated Arteries," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.47-59, 2024

• Open Access   Article

  Tsallis Holographic Dark Energy Cosmological Models in Modified Theory of Gravity

  V.M. Raut, A.S. Mankar, A.Y. Shaikh

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.60-65, Dec-2024

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  Abstract
  In the framework of f(R,T) gravity, this research aims to create Tsallis Holographic Dark Energy (THDE) models in a homogeneous and anisotropic Bianchi type-I model in Kasner form. We have employed two distinct volumetric expansions, Power law and exponential law, to determine the precise solutions of field equations. The conventional or conservative cosmological techniques, such as the deceleration parameter and the equation of state parameter, have been used to study the cosmic evolution. The physical characteristics of the model have been acquired. According to both expansion models, we have discovered that the universe is in the accelerating period and is reaching isotropy with delayed time. We also came to the conclusion that our model behaves similarly to a ?CDM model.

  Key-Words / Index Term
  Modified gravity, Bianchi type-I space-time in Kasner form, THDE

  References
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  Citation
  V.M. Raut, A.S. Mankar, A.Y. Shaikh, "Tsallis Holographic Dark Energy Cosmological Models in Modified Theory of Gravity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.60-65, 2024

• Open Access   Article

  Unsteady MHD Blood Flow Through Bifurcated Arteries with Heat Source and Magnetic Field in the Presence of Soret Effect

  Auwalu Alhassan Girema, Yusuf Ya’u Gambo, Bashir Yau Haruna

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.66-74, Dec-2024

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  Abstract
  This study explores unsteady blood flow in bifurcated arteries influenced by a constant transverse magnetic field and heat source. For easy analysis of axial velocity, temperature distribution, concentration of blood component and normal velocity, complex partial differential equations are transformed into ordinary differential equations by the method of separation of parameters subject to the conditions defined. Analytical solution illustrates how varying factors such as Hartmann number (Ha), Prandtl number (Pr), Schmidt number (Sc), Soret parameter (Sr) and Decay parameter (?) affect blood flow dynamics. The analysis was made using Matlab and the results are presented graphically for better understanding.

  Key-Words / Index Term
  The Blood Flow, Bifurcated Artery, Soret effect, Heat Source, Magnetic Field, Decay parameter

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  Citation
  Auwalu Alhassan Girema, Yusuf Ya’u Gambo, Bashir Yau Haruna, "Unsteady MHD Blood Flow Through Bifurcated Arteries with Heat Source and Magnetic Field in the Presence of Soret Effect," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.66-74, 2024

• Open Access   Article

  A Novel Iterative Approach to Optimize the Banach Contraction Method for Solving Systems of Integro-Differential Equations

  Thomas J.G., Okai J.O., Isah Abdullahi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.6 , pp.75-85, Dec-2024

  Abstract

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  Abstract
  This paper presents an Optimized Banach Contraction Method (OBCM), which employs a novel iterative technique to solve integro-differential equations (IDEs) and their systems. The method offers a more efficient and faster approach than traditional methods, eliminating the need for discretization, linearization, or restrictive assumptions. It provides both analytical and approximate solutions for linear and nonlinear equations, without requiring the computation of polynomials or Lagrange multipliers. These advantages improve the reliability of the OBCM, with numerical results confirming its effectiveness.

  Key-Words / Index Term
  Integro-differential equations (IDEs), Banach contraction principle, Variational iteration method, discretization, linearization

  References
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  Citation
  Thomas J.G., Okai J.O., Isah Abdullahi, "A Novel Iterative Approach to Optimize the Banach Contraction Method for Solving Systems of Integro-Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.75-85, 2024