Abstract
In this paper, we investigate the solution of fractional kinetic equation (FKE) associated with the incomplete I-function (IIF) by using the well-known integral transform (Laplace transform). The FKE plays a great role in solving astrophysical problems. The solutions are represented in terms of IIF. Next, we present some interesting corollaries by specializing the parameters of IIF in the form of simpler special functions and also mention a few known results, which are very useful in solving physical or real-life problems. Finally, some graphical results are presented to demonstrate the influence of the order of the fractional integral operator on the reaction rate.
Highlights
Arbitrary-order calculus (AOC) is a useful mathematical device that enables the study of arbitrary-order integrals and derivatives [1,2,3,4]
We simulate the numerical results for fractional kinetic equation (FKE) (25) at different values of various parameters presented in the form of Figures 1 and 2 by using Maple
We introduced generalized FKEs of the FKE associated with the incomplete I-functions and found their solutions in terms of incomplete I-functions
Summary
Arbitrary-order calculus (AOC) is a useful mathematical device that enables the study of arbitrary-order integrals and derivatives [1,2,3,4]. The expansions and generic nature of arbitrary-order kinetic equations associated with the fractional-order operators was well established in [6,7,8,9]. Since the last few decades, fractional kinetic equations in several shapes and configurations have been widely and productively employed in describing various significant problems of physics and astrophysics (see the recent papers [10,11,12,13,14,15,16,17]).
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