Volume-11 , Issue-3 , Jun 2024, ISSN 2348-4519 (Online)

• Open Access   Article

  Numerical Solutions of the SIRD Cholera Model Using the HPM and RKM Methods

  Munira Salisu, Mohammed Salahuddeen Atureta, Muhammad Manga

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.75-79, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this study we have modified SIRD model for the treatment of Cholera disease by the four control strategies such as the Vaccination, surveillance, washing of food items and therapeutic treatment. Using Homotopy perturbation method and the Runge kutta method. The susceptible class,Infected class and the recovered and the death category is being related with the homotopy perturbation method and the runge kutta method to observe the most efficient method to use to control the disease better.

  Key-Words / Index Term
  SIRD model, Susceptible, Infected, Recovered, Death, Runge kutta(order 4and order 5) method, Homotopy perturbation method

  References
  [1] A.A Ayoade and O.J Peter ‘’ on global stability of cholera model with prevention and control, Malaysian journal of computing ‘’ Vol.3(1) pp 28-36. 2018.
  [2] A.S. Mohammed and M.G salisu ‘’Global stability of SEIR model with holling type 11 incidence function : computational and mathematical methods in medicine.’’ Vol.2012 article ID 826052 pp1-8 2012.
  [3] B.O Akogwu, and J.O. Fatoba ‘’Numerical solutions of Covid 19 SIRD model in Nigeria’’. Vol. 6 no 4 pp 66-67 (2022).
  [4] D.N. Kwasi and C. Afriyel ‘’ control measures and the environment in the transmission dynamics of cholera’’ Vol. 2020 article ID 2485979 pp 1-16. 2020.
  [5] J.H. He’’ Comparison of homotopy perturbation method and homotopy analysis method’’. Applied mathematics and computation.. Vol 156 pp 527-539 .2004.
  [6] K.H. hantsa and B.N Kahsay.’’ Analysis of Cholera epidemic controlling using mathematical modelling’’ Vol. 2020 article ID 7369204 pp 1-14. 2020
  [7] M.A Islam ‘’Comparative study on numerical solutions of initial value problems ivp for ordinary differential equations (ODE) with Euler and Runge kutta method’’ Vol 5 pp 393-404. 2015.
  [8] N.K soopy,S Aman,K. Shah,H. Alarabiah and M.Arfan ‘’Mathematical analysis of SIRD model of COVID 19 with capputo fractional derivative based real data’’ Vol 103772 pp2211-3797.2020.
  [9] O.L Paride and H.mlyashimbi ‘’ fractional order model for cholera disease transmission with control strategies’’ Vol. 2022-R issue10 pp28919. 2020.
  [10] P.Panjah’’ optimal control analsys of a cholera model’’ Biophysical reviews and letters. Vol. 14(1) pp 27-48. 2021.

  Citation
  Munira Salisu, Mohammed Salahuddeen Atureta, Muhammad Manga, "Numerical Solutions of the SIRD Cholera Model Using the HPM and RKM Methods," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.75-79, 2024

• Open Access   Article

  An Advance towards Finding the Basic Feasible Solution and Optimal Solution in Transportation Problem

  Swati Dayma, Garima Singh, Manju Prabhakar

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.80-85, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized. It is also sometimes called as Hitchcock problem and solved a real life problem by using EQM method.

  Key-Words / Index Term
  Transportation Problem, Initial Basic Feasible

  References
  [1] B. Mallia, M. Das, C. Das “Fundamentals of Transportation Problem”, International Journal of Engineering and Advanced Technology (IJEAT) ISSN: Volume-10 Issue-5, 2021.
  [2] Cheng, L., De Vos, J., Witlox, F. “Transport modes and sustainability”. In Vickerman R.W. (ed) International Encyclopedia of Transportation . Elsevier, forthcoming, 2021.
  [3] Firas Hamid Thanoon “Proposed Method for Solving Transportation Problems”, Wasit Journal for Pure Sciences Vol. 1, 2022.
  [4] J.K. Sharma “Operation research theory and application” Laxmi Publication ; Sixth Edition pp.256-309, 2017.
  [5] J. Opara, P.A. Esemokumo, R. Bekesuoyeibo “A New Algorithm for Reaching an Optimal Solution to a Nonlinear Transportation Problem”, International Journal of Scientific Research in Mathematical and Statistical Sciences Volume-9, Issue-2, pp.12-16, 2022.
  [6] L. Elaine Y. Man, and Adam B. “A Qualitative Approach of Identifying Major Cost Influencing Factors in Palm Oil Mills and the Relations towards Production Cost of Crude Palm Oil”, American Journal of Applied Sciences, vol. 8, pp. 441-446, 2011.
  [7] M. K. Islam, M. F. Uddin, M. M. Alam, G. M. O. Faruque4 “A Mixed Integer Linear Programming Approach for Two Stage Supply Chain Network Coordination of Agricultural Products Considering Uncertainty”, International Journal of Scientific Research in Mathematical and Statistical Sciences Vol.6, Issue.6, pp.36-45, 2019.
  [8] Norozi A., Ariffin M. K. A., and Ismail N. “Application of Intelligence Based Genetic Algorithm for Job Sequencing Problem on Parallel Mixed-Model Assembly Line”, American Journal of Engineering and Applied Sciences, 3, pp.15-24, 2010.
  [9] N. Sen et al. “Mathematical Modeling of Transportation Related Problem of Southern Assam and Its Optimal Solution” AUJ Science, Vol. 31, pp.22-27, 2008a, 2008b, 2008c.
  [10] S. Mishra “Solving Transportation Problem by Various Methods and Their Comparison”. International Journal of Mathematics Trends and Technology, vol. 44, pp.270 – 275, 2017.
  [11] S.K. Goyal “Improving VAM for unbalanced transportation problems”, Journal of Operational Research Society, pp. 1113-1114, 1984.
  [12] T.C. Koopmans “Optimum Utilization of Transportation System”, Econometrica Supplement vol.17, 1949.

  Citation
  Swati Dayma, Garima Singh, Manju Prabhakar, "An Advance towards Finding the Basic Feasible Solution and Optimal Solution in Transportation Problem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.80-85, 2024

• Open Access   Article

  Exploring Sum Divisor Cordial Labeling Techniques across Various Graph Structures

  U.M. Prajapati, P.A. Patel

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.86-91, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  This study explores the probability of various graphs being identified as sum divisor cordial graphs. The graphs examined include the Holiday star graph , Christmas star graph , Lilly graph , Eight sprocket graph , Torch graph , Arm crown and graph created by attaching cycle at each outer vertex of circular ladder graph . The results indicate that applying sum divisor cordial labeling demonstrates that these graphs possess the characteristics of sum divisor cordial graphs.

  Key-Words / Index Term
  Cordial Labeling; Cordial Graphs; Divisor Cordial Labeling; Divisor Cordial Graphs; Sum Divisor Cordial Labeling; Sum Divisor Cordial Graphs.

  References
  [1] F. Harary, “Graph Theory”, Addition-Wesley, Reading, Mass, Vol.4, Issue.4, pp.103-110, 1972.
  [2] J. A. Gallian, “A Dynamic Survey of Graph Labeling”, In the Electronic Journal of Combinatorics, 1-644, 2023.
  [3] R. Varatharajan, S. Navanaeethakrishnan and K. Nagarajan, “Divisor Cordial Graphs”, International Journal of Mathematical Combinatorics, Vol.4, Issue.4, pp.15-25, 2011.
  [4] M. I. Bosmia and K. K. Kanani, “Divisor Cordial Labeling in the Context of Graph Operationson Bistar”, Global Journal of Pure and Applied Mathematics, Vol.12, Issue.3, pp.2605-2618, 2016.
  [5] U. M. Prajapati and P. A. Patel, “Divisor Cordial Labeling in the Context of Friendship Graph”, 5th Edition, Journal of Xidian University, Vol.14, Issue.5, pp.167-177, 2020.
  [6] A. Lourdusamy and F. Patrick, “Sum Divisor Cordial Graphs”, Proyecciones J. of Math, Vol.35, Issue.10, pp.119-136, 2016.
  [7] A. H. Rokad, “Subtract Divisor Cordial Labeling of Ring Sum of a Graphs”, Research &Reviews, Discrete Mathematical Structures, Vol.6, Issue.3, pp.23-28, 2020.
  [8] D. G. Adalja1 and G. V. Ghodasara, “Subtract Divisor Cordial Labeling of Ring Sum of a Graph With Star Graph”, Int. J. of Comp. Sci.and Eng, Vol.6, Issue.6, pp.1567-1573, 2018.
  [9] U. M. Prajapti and R. M. Gajjar, “Labeling Techniques of Holiday Star Graph”, International J. of Math Trends and Technology, Vol.49, Issue.6, pp.339-344, 2018.
  [10] U. M. Prajapti and R. M. Gajjar, “Some Labeling Techniques of Christmas Star Graph”, International J. of Math and Soft Computing, Vol.8, Issue.2, pp.01-09, 2018.
  [11] S. Sripriya and K. Ramachandran, “Total Neighbourhood Prime Labeling of Certain Graphs”, In Journal of Physics: Conference Series, Vol.1377, Issue.1, pp.012037, 2019.
  [12] V. J. Kaneria and J. C. Kanani, “Graceful Labeling for Eight Sprocket Graph”, In Recent Advancements in Graph Theory, pp.1-8, 2020.
  [13] J. M. Manulang and K. A. Sugeng, “Graceful labeling on torch graph”, Indonesian Journal of Combinatorics, Vol.2, Issue.1, pp.14-19, 2018.
  [14] D. B. West, “Introduction to graph theory”, Upper Saddle River: Prentice hall, Vol.2, Issue.2, 2001.

  Citation
  U.M. Prajapati, P.A. Patel, "Exploring Sum Divisor Cordial Labeling Techniques across Various Graph Structures," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.86-91, 2024

• Open Access   Article

  Riemann Mapping Theorem as a Conformal mapping Methods in solving Dirichlet Boundary Value Problems and its’ Application

  I O Ismaila, N H Manjak, A D Hina

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.92-96, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  This study started by illustating the Riemann Mapping Theorem and find also finding a function that is harmonic on the unit disc to the upper half plane and vice-versa using an inverse map with the help of a self conformal map and we discovered that those self map and its inverse are both harmonic. We were able to map the sector onto the upper half plane with the help of conformal self map which was transform back the unit disc by taking its inverse . Further, we showed the application of Riemann Mapping Theorem on steady state temperature in a thin infinite plate onto the upper half plane since there are three points of discontinuity on that steady state temperature by using a best conformal map and then removing all points of discontinuity before obtaining our result then transforming back to the original plane since it has the same conformal mapping property.

  Key-Words / Index Term
  conformal map, self map, upper half plane, unit disc, Riemann map, dirichlet problem, boundary value problem

  References
  [1] L.V Ahlfors. ‘Complex Analysis’, McGraw-Hill, New York, Vol. 3, issue 1, 1979.
  [2] T. W. Gamelin. ‘Complex Analysis’ (Rev ed.), Springer, New York, Vol.1, Issue.2, 2001.
  [3] R. C. Gunning. ‘Lectures on Riemann Surfaces’, Princeton, New Jersey, Vol.3, Issue.1, 1966.
  [4] W. F. Osgood. ‘On the Existence of The Green’s Function For the Most General Simply Connected Plane Region’, Trans. Amer. Math. Soc. Vol.1, Issue 1, pp.310-314, 1900.
  [5] R.Walter. ‘Principles of Mathematical Analysis’, McGraw-Hill, New York, Vol. 3, issue 2, pp. 270-276, 1976.
  [6] J. L. Walsh, ‘History of the Riemann Mapping Theorem’, The American Mathematical Monthly, vol. 80, , Issue.2, pp. 270-276, 2018 https://doi.org/10.1080/00029890.1973.11993266
  [7] L. Bingyuan: ‘The Green`s Function Method for the Riemann Mapping Theorem’: Handbook of Complex Analysis CRC Press Vol.1, Issue.2, pp.1-4, 2022
  [8] I. O. Ismaila, N. H. Manjak, A. M. Kwami, ‘Application of Schwartz Christoffel Transformation as a Conformal Map in Solving Some Physical Problems’ International Journal of Scientific Research in Physics and Applied Sciences, ISROSET Vol.12, Issue.2, pp.47-54, 2024.
  [9] V. V. Datar, ‘Riemann Mapping Theorem’, Lecture Note on Riemann Mapping Theorem, vol. 1 Issue 1 pp. 1-7, 2016.
  [10] W. ALEXANDER, ‘Riemann Mapping Theorem’, Lecture Note on Riemann Mapping Theorem, vol.2, Issue 1, pp. 1-11, 2023.

  Citation
  I O Ismaila, N H Manjak, A D Hina, "Riemann Mapping Theorem as a Conformal mapping Methods in solving Dirichlet Boundary Value Problems and its’ Application," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.92-96, 2024

• Open Access   Article

  A Study of Contour Integration: Methods and Their Applications

  Urvashi Yadav, Payal Shrivastava, Garima Singh

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.97-102, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Complex analysis is a branch of mathematics that explores functions of complex numbers which consist of real and an imaginary part. One of its powerful techniques is contour integration , a technique for calculating integrals by following designated paths , or contour in the complex plane . This approach allows us to integrate functions that might be difficult or impossible to tackle using traditional real -variable methods .Contour integration and residues are indeed in complex analysis ,which are measure of functions behavior near its singularities ( points where the functions is not defined or is infinitely large )by using residue theorem ,a key principle in complex analytic ,we can measure complex integrals by combining the residues at these singularities , simplifying what might otherwise be a challenging problem .This technique finds applications in various fields ,including mathematics ,physics , engineering.

  Key-Words / Index Term
  Contour , Contour integration, Cauchy integral Theorem, Residue theorem, Singularity

  References
  [1] Ali Dhurgham Azeez, Iraq,” A Study on Method of Contour Integration” International Journal of Research, Vol.3, Issue.14, pp.1-4, 2016.
  [2] Abdulsattar, A.H,” A study of contour integration of complex analysis” International Journal, pp.622-639, 2017.
  [3] Bak, J. and Newman,D.J, “ applications of residue theorem to the evaluation of integrals and sums,” pp.156-205, 2010.
  [4] Coleman,”A contour formulation of plane creeping Newton flow “. The Quarterly Journal of Mechanics and Applied Mathematics, pp.453-464, 1981.
  [5] Farrell “Evaluating Certain Real Integrals by Cauchy ‘s Residue Theorem” . The American Mathematical Monthly , pp. 151-152, 1961 .
  [6 ] He Mingxuan , “Applications of Residue Theorem in Some Real
  Integral Calculations”. Mathematical Learning and Research, pp.138-139, 2021.
  [7] John D. Dixon “, A brief proof of Cauchy ‘s integral Theorem” pp. 625-626.
  [8] Walter Rudin,” Real and complex analysis ”Third edition MeGraw-Hill, 1987.
  [9] Xu Jianzhong .”Application of Residue Theorem in Real Integrals”. Journal of Xichang University , pp.57- 59, 2018.
  [10] Zeng Qiao “Exploring the application of residue theorem in solving different types of integrals” .Science and Technology Innovation and Application , pp.175-176, 2020.
  [11] DR. H.K Pathak , Complex Analysis ,Shiksha Sahitya Prakashan, pp.302-306.

  Citation
  Urvashi Yadav, Payal Shrivastava, Garima Singh, "A Study of Contour Integration: Methods and Their Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.97-102, 2024

• Open Access   Article

  Telescoping Decomposition Method for Solving Parabolic-Hyperbolic Nonlinear Partial Differential Equations

  Clement Elkana, Manjak N.H, Kwami A.M

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.103-108, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The aim of this paper is to study the Telescoping Decomposition Method to solve Parabolic-Hyperbolic nonlinear partial differential equations in one dimension. The Telescoping Decomposition Method (TDM) is a new iterative method to obtain numerical and analytical solutions for first order and second order non-linear differential equations. It is a modified form of the well-known Adomian Decomposition Method (ADM).

  Key-Words / Index Term
  Telescoping Decomposition Method,Adomian Decomposition Method,Adomian Polynomial, Parabolic-Hyperbolic equations, on-linear equations and Differential operators.

  References
  [1] A.Wazwaz, ‘A Reliable modification of Adomian decomposition method’. Appl. Math. And comput. Vol. 102, issue 1, pp. 77-80, 1999.
  [2] A.A Hemeda, ‘Variational Iteration Method for solving nonlinear partial differential equation’pp 501-511, 2007.
  [3] A. Wazwaz, ‘A new algorithm for calculating Adomian polynomials for nonlinear equation’s, Elservier, Applied mathematics and computation 111,53-69, 2000
  [4] G. Adomian, ‘A Review of the decomposition Method in Mathematics’. Journal of Mathematical Analysis and Applications pp135:501-544, 1988
  [5] G. Adomian, ‘A review of the Decomposition method and some recent results for nonlinear equations’, a jounal of mathematics and . Computing model pp 137:17-43, 1992.
  [6] H. Ahmed ‘Adomian Decomposition Method:convergence Analysis and Numerical Approximations’. Master of science mathematics,pp 401-432 2008.
  [7] J. Badran ‘Numerical solution of Drinfeld-Sokolov-Wilso system by using Modified Adomian Decomposition Method’pp 22-35 2021.
  [8] J. Biazar, H. Ibrahim, ‘An Approximation to the solution of Hyperbolic Equation by Adomian Decomposition Method and comparison with characteristics methods’. Applied Mathematics and computing pp163:633-638, 2005.
  [9] J. Biazar, Z. Ayati, ‘An approximation to the solution of parabolic equation by Adomian Decomposition Method and comparing the result with Crank-Nicolson Method’pp 39:1925-1933, 2006.
  [10] K. Al- Dosary, N.Al- Jubouri, H. Abdullah .‘On the solution of Abel Differential Equation by Adomian Decomposition method’, Journal of applied mathematics, Vol.2,no. 43:2105- 2118, 2008.

  Citation
  Clement Elkana, Manjak N.H, Kwami A.M, "Telescoping Decomposition Method for Solving Parabolic-Hyperbolic Nonlinear Partial Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.103-108, 2024

• Open Access   Article

  LRS Bianchi type-I Universe with anisotropic dark energy and special form of deceleration parameter in f(Q) Gravity

  R.P. Wankhade

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.109-114, Jun-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, LRS Bianchi-I space-time is considered in the presence of perfect fluid source in the frame work of teleparallel gravity which is so called f(Q) gravity, where f(Q) is the function of non-metricity scalar Q. This non-metricity scalar Q is responsible for the gravitational interaction. We have considered a special form of the f(Q) function which is given as f(Q) = ?Qn, (where ? and n both are the dynamical model parameters). The Einstein’s field equations have been solved by taking into account the special form of deceleration parameter. The geometrical and physical aspect of the model is also studied. We find that the model has initial singularity and the physical parameters diverge at the initial epoch. The model resemble ?CDM model for large time t.

  Key-Words / Index Term
  LRS Bianchi type-I space-time, Special form of deceleration parameter, f(Q) gravity.

  References
  [1] A. G. Riess et al., “BVRI light curves for 22 type Ia supernovae”: The Astronomical Journal, Vol. 117, pp. 707-724, 1999.
  [2] S. Perlmutter et al., “Measurements of ? and ? from 42 high-redshift supernovae”: The Astrophysical Journal, Vol. 517, pp. 565-586, 1999.
  [3] C. L. Bennett et al. “First-year Wilkinson microwave anisotropy probe (wmap)* observations: foreground emission”: The Astrophysical Journal Supplement Series, Vol.148, pp. 97–117, 2003.
  [4] D. N. Spergel et al. “First-year Wilkinson Microwave Anisotropy Probe (WMAP)* observations: determination of cosmological parameters”: The Astrophysical Journal Supplement Series, Vol.148, pp. 175–194, 2003.
  [5] M. Tegmark et al. “Cosmological parameters from SDSS and WMAP”: Physical Review D, Vol. 69, Issue 10, pp. 103501-103526, 2004.
  [6] M. Tegmark et al. “The three-dimensional power spectrum of galaxies from Sloan digital sky survey”: The Astrophysical Journal, Vol.606, pp. 702-740, 2004.
  [7] S. Weinberg, “The cosmological constant problem”: Review of Modern Physics, Vol.61, Issue 1, pp. 1-23, 1989.
  [8] S. M. Carroll, “The cosmological constant”: Living Reviews in Relativity, Vol. 4, pp.1-56, 2001.
  [9] P. J. E. Peebles and B. Ratra, “The cosmological constant and dark energy”: Review of Modern Physics, Vol. 75, pp. 559-606, 2003.
  [10] T. Padmanabhan, “Cosmological constant-the weight of the vacuum”: Physics Reports, Vol. 380, Issue 5-6, pp. 235-320, 2003.
  [11] S.M. Carroll, V. Duvvuri, M. Trodden, M.S. Turner, “Is cosmic speed-up due to new gravitational physics?”: Physical Review D, Vol. 70, Issue 4, pp.043528-043532, 2004.
  [12] S. Capozziello, S. Nojiri, S.D. Odintsov, A. Troisi, “Cosmological viability of f (R)-gravity as an ideal fluid and its compatibility with a matter dominated phase’’: Physics Letter B, Vol. 639, Issue 3-4, pp.135-146, 2006.
  [13] S. Nojiri, S.D. Odintsov, “Dark energy cosmology from higher-order, string-inspired gravity, and its reconstruction”: Physical Review D, Vol.74, Issue 4, pp. 046004-046018, 2006.
  [14] S.H. Hendi, D. Momeni, “Black-hole solutions in F(R) gravity with conformal anomaly’’: The European Physical Journal C, Vol. 71, pp.1823-1835, 2011.
  [15] M. Sharif, S. Arif, “Non-vacuum static cylindrically symmetric solution and energy distribution in f(R) gravity’’: Astrophysics and Space Science, Vol. 342, pp. 237-243, 2012.
  [16] S. Nojiri, S.D. Odintsov, “The new form of the equation of state for dark energy fluid and accelerating universe’’: Physics Letter B, Vol. 631, Issue 3-4, pp. 144-150, 2006.
  [17] S. Nojiri, S.D. Odintsov, “Unified cosmic history in modified gravity: from F (R) theory to Lorentz non-invariant models’’: Physics Reports, Vol. 505, Issue 2-4, pp. 59-144, 2011.
  [18] G. Cognola, M. Gastaldi, S. Zerbini, “On the stability of a class of modified gravitational models’’: International Journal of Theoretical Physics, Vol. 47, pp. 898-910, 2008.
  [19] S. Nojiri, S.D. Odintsov, P.V Tretyakov, “From inflation to dark energy in the non-minimal modified gravity’’: Progress of Theoretical Physics Supplement, Vol. 172, pp. 81–89, 2008.
  [20] N.M. Garcia, F.S.N. Lobo, J.P. Mimoso, “f(G) modified gravity and energy conditions” : Journal of Physics: Conference Series 314, pp. 012056, doi:10.1088/1742-6596/314/1/012056, 2011.
  [21] K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, “Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests’’: Astrophysics and Space Science, Vol. 342, pp.155-228, 2012.
  [22] M. Jamil, D. Momeni, R. Myrzakulov, “Stability of a non-minimally conformally coupled scalar field in F(T) cosmology’’: The European Physical Journal C, Vol. 72, pp.2075, 2012.
  [23] M. Jamil, K. Yesmakhanova, D. Momeni, R. Myrzakulov, “Phase space analysis of interacting dark energy in f(T) cosmology’’: Central European Journal of Physics, Vol. 10, Issue 5, pp.1065-1071, 2012.
  [24] T. Harko, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, “f(R,T) gravity’’: Physical Review D, Vol.84, pp. 024020-024031, 2011.
  [25] R. P. Wankhade, A.S. Bansod, “LRS Bianchi type-I universe with anisotropiv dark energy and special form of deceleration parameter in f(R,T) gravity”: International Journal of Advanced Astronomy, Vol. 6, Issue 1, pp. 1-4, 2018.
  [26] R. P. Wankhade et. al., “Cosmological Model with Time Varying Cosmological Constant, Quadratic Equation of State and Special form of Deceleration Parameter in f (R, T) Gravity’’: International Journal of Scientific Research in Science and Technology, Vol.10, Issue 3, pp.503-513, 2023.
  [27] S. Mandal et al., “Cosmography in f(Q) gravity’’, Physical Review D, Vol. 102, pp.124029, 2020.
  [28] S. Mandal et al., “Energy conditions in f(Q) gravity’’, Physical Review D, Vol. 102, pp.024057, 2020.
  [29] W. Khyllep, A. Paliathanasis, and J. Dutta, “Cosmological solutions and growth index of matter perturbations in f(Q) gravity’’, Physical Review D, Vol. 103, pp.103521, 2021.
  [30] T. Harko et al., “Coupling matter in modified Q gravity’’: Physical Review D, Vol. 98, pp.084043, 2018.
  [31] S. H. Shekh, “Models of holographic dark energy in f (Q) gravity’’, Physics of the Dark Universe, Vol. 33, pp.100850, 2021.
  [32] T. Harko et al., “Comment on reexamining f(R,T) gravity’’: Physical Review D, Vol. 101, pp.108501, 2020.
  [33] M. Koussour et al., “Thermodynamical aspects of Bianchi type-I Universe in quadratic form of f (Q) gravity and observational constraints’’: Journal of High Energy Astrophysics, Vol. 37, pp. 15-24, 2023.
  [34] D.R.K. Reddy, R. Santikumar, R.L. Naidu, “Bianchi type-III cosmological model in f(R,T) theory of gravity’’: Astrophysics and Space Science, Vol. 342, pp. 249-252, 2012.
  [35] D.R.K. Reddy, R.L. Naidu, B. Satyanarayana, “Kaluza-Klein Cosmological Model in f(R,T) Gravity’’: International Journal of Theoretical Physics, Vol. 51, pp. 3222-3227, 2012.
  [36] N. Banerjee, S. Das, “Acceleration of the universe with a simple trigonometric potential’’: General Relativity and Gravitation, Vol. 37, pp. 1695-1703, 2005.
  [37] N. Aghanim et al., “Planck 2018 results-VI. Cosmological parameters’’: Astronomy and Astrophysics, Vol. 641, A1, pp. 1-56, 2020.
  [38] A. Singha, U. Debnath, “Accelerating universe with a special form of decelerating parameter’’: International Journal of Theoretical Physics, Vol. 48, pp.351-356, 2009.
  [39] S. Capozziello et al., “Cosmological viability of f(R) gravity as an ideal fluid and its compatibility with a matter dominated phase”: Physics Letter B, Vol. 639, pp. 135-143, 2006.
  [40] R. D. Blandford et al., “Two-dimensional adiabatic flows on to a black hole – I. Fluid accretion’’: Monthly Notices of the Royal Astronomical Society, Vol. 349, Issue 1, pp. 68–86, 2004.
  [41] T. Chiba, T. Nakamura, “The luminosity distance, the equation of state, and the geometry of the universe’’: Progress in Theoretical Physics, Vol. 100, pp. 1077-1082, 1998.
  [42] V. Sahni, “The cosmological constant problem and quintessence’’: Classical Quantum Gravity, Vol.19, No. 13, pp.3435, 2002.
  [43] M. Visser, “Jerk, snap and the cosmological equation of state’’: Classical Quantum Gravity, Vol. 21, No. 11, pp. 2603, 2004.
  [44] M. Visser, “Cosmography: Cosmology without the Einstein equations’’: General Relativity and Gravitation, Vol. 37, pp. 1541-1548, 2005.
  [45] K.A. Bronnikov, E.N. Chudaeva, G.N. Shikin, “Magneto-dilatonic Bianchi-I cosmology: Isotropization and singularity problems’’: Classical Quantum Gravity, Vol. 21, No. 14, pp. 3389, 2004.

  Citation
  R.P. Wankhade, "LRS Bianchi type-I Universe with anisotropic dark energy and special form of deceleration parameter in f(Q) Gravity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.109-114, 2024