Abstract
Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.
Highlights
In 2011, Srivastava et al [41, p.491, Eq(1.20)] introduced and studied the following extension of the generalized Hurwitz-Lerch Zeta function:
The Hurwitz-Lerch Zeta function is de...ned by [34, 35]:X 1 n ( ; m; ) = (n + )m (1) n=0Many researchers studied many di¤erent generalisations and extensions of the Hurwitz-Lerch Zeta function by inserting certain additional parameters to the series representation of the Hurwitz-Lerch Zeta function
The results obtained in this study have remarkable signi...cance as the solution of the equations are general and can be reproduced many new and known solutions of (FKEs) involving various type of special functions
Summary
In 2011, Srivastava et al [41, p.491, Eq(1.20)] introduced and studied the following extension of the generalized Hurwitz-Lerch Zeta function: (x > 0; 0): The fractional generalisation of the standard kinetic equation (5) is studied by Haubold and Mathai as follows [23]: (x) 0 = c 0 Dx 1 (x) and acquired the solution of (4) as follows: X 1 (x) = 0 ( 1 )k (cx) k : ( k +1)
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