Abstract
The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function E^{gamma,rho}_{k,zeta,eta}(cdot). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.
Highlights
1 Introduction and preliminaries The fractional-order calculus (FOC) constitutes a branch of mathematics dealing with differentiation and integration under an arbitrary order of the operation, that is, the order can be any real or even complex number, the integer one [1,2,3,4,5,6,7,8,9]
According to [10, 12], the reason why FOC remained practically unexplored for engineering applications and why only pure mathematics was privileged to deal with it for so long time can be seen in multiple definitions of FOC, missing simple geometrical interpretation, the absence of solution methods for fractional-order differential equations and seeming adequateness of the integer-order calculus (IOC) for majority of problems
The objective of this paper is to derive the solution of the fractional kinetic equation involving the generalized k-Mittag-Leffler function
Summary
Introduction and preliminariesThe fractional-order calculus (FOC) constitutes a branch of mathematics dealing with differentiation and integration under an arbitrary order of the operation, that is, the order can be any real or even complex number, the integer one [1,2,3,4,5,6,7,8,9]. Given a function f with an (n – 1)th absolutely continuous derivative, Caputo defined the fractional derivative by A fractional generalization of the standard kinetic equation (1.5) is given by Haubold and Mathai [26] as follows: N (τ ) – N0 = – υ 0D–τ 1N (τ ).
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