Full Paper View Go Back

Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function

Javid Majid1 , Imtiyaz Majid2

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.94-101, Dec-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.94101


Online published on Dec 31, 2018


Copyright © Javid Majid, Imtiyaz Majid . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library


XML View     PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: Javid Majid, Imtiyaz Majid, “Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.94-101, 2018.

MLA Style Citation: Javid Majid, Imtiyaz Majid "Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.6 (2018): 94-101.

APA Style Citation: Javid Majid, Imtiyaz Majid, (2018). Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(6), 94-101.

BibTex Style Citation:
@article{Majid_2018,
author = {Javid Majid, Imtiyaz Majid},
title = {Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {12 2018},
volume = {5},
Issue = {6},
month = {12},
year = {2018},
issn = {2347-2693},
pages = {94-101},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=979},
doi = {https://doi.org/10.26438/ijcse/v5i6.94101}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i6.94101}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=979
TI - Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Javid Majid, Imtiyaz Majid
PY - 2018
DA - 2018/12/31
PB - IJCSE, Indore, INDIA
SP - 94-101
IS - 6
VL - 5
SN - 2347-2693
ER -

438 Views    219 Downloads    157 Downloads
  
  

Abstract :
In this paper we will implement the generalized fractional operators induced by Saego-Maeda using the Appell’s F_3 (.) function and set up the image formulas associated with the generalized Miller-Ross function in terms of the generalized Fox- Wright function. We will also employ certain integral transforms on the results obtained from the differentials and the integrals and present some more image formulas.

Key-Words / Index Term :
Generalized Miller-Ross function, Saego-Maeda fractional operator, Fox Wright function

References :
[1] D. Baleanu, O. G. Mustafa, “On the Global Existence of Solutions to a Class of Fractional Differential Equations”, Com. Math. Appl, Vol. 59 pp.1835-1841. 2010
[2] D. Baleanu, P. Agarwal, S. D. Purohit, “Certain fractional integral formulas involving the product of generalized Bessel functions”, Sci. World J. pp.1-9, 2013
[3] A.A. Kilbas, “Fractional Calculus of the Generalized Wright Function”, Fract. Calc. Appl. Anal, vol.8 No.2 pp.113-126, 2005
[4] Miller, K. And Ross, B., “An introduction to the Fractional Calculus and Fractional differential Equations”, John Wiley Sons, New York,1993.
[5] Saigo M., “A Remark on Integral Operators Involving the Gauss Hyper-geometric Functions” Math. Rep. College General Ed. Kyushu Univ., Vol. 11, pp. 135-143, 1978
[6] G.M. Mittag-Leffler, “Sur la representation analytique de’une branche Uniforme une function monogene”, Acta. Math., 29, pp.101-181. 1905
[7] T.R. Prabhakar, ”A Singular Integral Equation with a Generalized Mittag-Leffler Function in the Kernel”, Yokohama Math. J., vol 19, pp.7-15, 1971
[8] D. Kumar, S. D. Purohit, J. Choi, “Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials”, J. Nonlinear Sci. Appl, 9 821, 2016
[9] J. Ram, D. Kumar, “Generalized fractional integration involving Appell hyper-geometric of the product of two H-functions”, Vijnana Parishad Anusandhan Patrika, Vol. 54,No.3 pp. 33-43, 2011
[10] J. Zhao, “Positive solutions for a class of q-fractional boundary value problems with p-Laplacian”, J. Nonlinear Sci.Appl., 8 , 442-450.1, 2015
[11] P. Agarwal, J. Choi, R. B. Paris, Extended Riemann-Liouville fractional derivative operator and its applications. Nonlinear Sci. Appl. Vol. 8 ,pp. 451-466, 2015
[12] R. K. Saxena, J. Ram, D. Kumar, “Generalized fractional integration of the product of Bessel functions of the First kind”, Proceedings of the 9th Annual Conference, Soc. Spec. Funct. Appl., vol.9 , pp.15-27, 2011
[13] S. D. Purohit, S. L. Kalla, D. L. Suthar, “Fractional integral operators and the multi index Mittag-Leffler functions”, Sci. Ser. A Math. Sci. ,vol. 21,pp. 87-96, 2011
[14] S. D. Purohit, D. L. Suthar, S. L. Kalla, “Marichev-Saigo-Maeda fractional integration operators of the Bessel function”, Matematiche (Catania), 67 ,pp. 21-32, 2012
[15] S. R. Mondal, K. S. Nisar, “Marichev-Saigo-Maeda fractional integration operators involving generalized Bessel function’s”, Math. Probl. Eng., vol. 11 pages.1-9, 2014
[16] Javid Majid, Imtiyaz, Aarif and Jain, “Certain image formulas associated with the fractional integrals and derivatives of the product of Srivstava polynomials and the K-function”, IJRAR ,Vol. 5,issue 4,pages 32-47,2018
[17] Shweta Pandey, Sandeep Dixit, ‘Solution of System of Fractional Differential equations using Variational Iteration Method”, International Journal of Computer Sciences and engineering, Vol. 6, Issue 8,pp. 797-802,2018.
[18] Saigo M., “A Remark on Integral Operators Involving the Gauss Hyper-geometric Functions” Math. Rep. College General Ed. Kyushu Univ., Vol. 11, pp. 135-143, 1978
[19] Appell, P. and Kampe de Feriet, J., “Functions Hyper-geometriqueset Hyperspheriques Polynomes d`Hermite” . Gauthier-Viliars, Paris. 1926
[20] Wright E. M., “The asymptotic expansion of the generalized hyper-geometric functions” J. London Math. Soc., Vol. 10, pp. 286-293, 1935
[21] Rainville E. D., “Special Functions”, the Macmillan Company, New York, 1963
[22] Farhan, Sharma and Jain, “Generalized Miller-Ross Function and its Integral Representation”, International Journal of Mathematics Trends and Technology- Vol. 16 Number 1, pp. 16-18,2014
[23] Mathai AM, Saxena RK, Haubold HJ. “The H-Function Theory and Applications” New York, NY: Springer-Verlag 2010
[24] I.N.Sneddon, “The use of integral transforms”, Tata McGraw- Hill, New Delhi, 1979

Authorization Required

 

You do not have rights to view the full text article.
Please contact administration for subscription to Journal or individual article.
Mail us at  support@isroset.org or view contact page for more details.

Go to Navigation