Generalized Integral Transform and Fractional Calculus Involving Extended pRq(α β Ζ) Function

Jump To References Section

Authors

  • Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, 395 007 ,IN
  • Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, 395 007 ,IN
  • Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, 395 007 ,IN

DOI:

https://doi.org/10.18311/jims/2022/29310

Keywords:

Generalized hypergeometric function, Wright hypergeometric function, Generalized integral transforms, k-Pochhammer symbol, Pathway fractional hypergeometric integral operator

Abstract

In this paper, we address an extended version of pRq(? ? ?) function using k-Pochhammer symbol and study their classical properties and generalized integral transform. Further, we study Pathway fractional hypergeometric integral and fractional derivatives of the extended pRq(? ? ?) function. Some special cases have also been illustrated.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2022-01-27

How to Cite

Pal, A., Jana, R. K., & Shukla, A. K. (2022). Generalized Integral Transform and Fractional Calculus Involving Extended <sub>p</sub>R<sub>q</sub>(α β &#918;) Function. The Journal of the Indian Mathematical Society, 89(1-2), 100–116. https://doi.org/10.18311/jims/2022/29310
Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

References

R. Desai and A. K. Shukla, Some results on function pRq( , ; z), J. Math. Anal. Appl., 448 (2017), 187–197. DOI: https://doi.org/10.1016/j.jmaa.2016.10.048

R. Desai and A. K. Shukla, Note on pRq( , ; z) function, J. Indian Math. Soc., 88(3-4) (2021), 288–297. DOI: https://doi.org/10.18311/jims/2021/27835

R. D´?az and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15 (2007), 179–192.

A. Erd´elyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. II, McGraw-Hill Book Company, New York, 1954.

A. A. Kilbas and N. Sebastian, Generalized fractional differentiation of Bessel function of the first kind, Math. Balkanica (New Ser.) 22 (2008), 323-346.

A. M. Mathai and H. J. Haubold, Pathway model, superstatistics, Tsallis statistics and a generalize measure of entropy, Phys. A., 375 (2007), 110–122. DOI: https://doi.org/10.1016/j.physa.2006.09.002

S. S. Nair, Pathway fractional integration operator, Fract. Calc. Appl. Anal. 12(3) (2009), 237–252.

D. H. Nair, On a class of fractional integral operator through pathway idea, Proc. 12th Annual Conf. SSFA, 12 (2013), 91–109.

T. Pohlen, The Hadamard Product and Universal Power Series. Ph.D. Thesis, Universit¨at Trier, Trier, Germany, 2009.

T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7–15.

E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11 (1978), 135–143.

S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordan and Breach, New York, 1993.

M. Sharma and R. Jain, A note on a generalized M-series as a special function of fractional calculus, Fract. Calc. Appl. Anal., 12(4) (2009), 449–452.

K. Sharma, Application of fractional calculus operators to related areas, Gen. Math. Notes, 7(1) (2011), 33–40.

N. Virchenko, On the generalized conuent hypergeometric function and its applications, Fract. Calc. Appl. Anal., 9(2) (2006), 101–108.

N. Virchenko, On some generalizations of classical integral transforms, Mathematica Balkanica, 26(1-2) (2012), 257–264.

E. M. Wright, On the coefficient of power series having exponential singularities, J. Lond. Math. Soc., 5 (1933), 71–79. DOI: https://doi.org/10.1112/jlms/s1-8.1.71