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Generalized Fractional Integral Operators and M-Series


Affiliations
1 Department of Mathematics, JIET Group of Institutions, Jodhpur 342002, India
2 Department of Mathematics and Statistics, J. N. V. University, Jodhpur 342002, India
3 Department of Mathematics, Kota University, Kota 324005, India
4 Department of Mathematics, Poornima University, Jaipur 302022, India
 

Two fractional integral operators associated with Fox H-function due to Saxena and Kumbhat are applied to M-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function pFq. The Mellin and Whittaker transforms are obtained for these compositional operators with M-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms of H-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries.

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  • Generalized Fractional Integral Operators and M-Series

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Authors

A. M. Khan
Department of Mathematics, JIET Group of Institutions, Jodhpur 342002, India
R. K. Kumbhat
Department of Mathematics and Statistics, J. N. V. University, Jodhpur 342002, India
Amit Chouhan
Department of Mathematics, Kota University, Kota 324005, India
Anita Alaria
Department of Mathematics, Poornima University, Jaipur 302022, India

Abstract


Two fractional integral operators associated with Fox H-function due to Saxena and Kumbhat are applied to M-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function pFq. The Mellin and Whittaker transforms are obtained for these compositional operators with M-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms of H-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries.

Keywords


English