Generalized Fractional Kinetic Equations Involving the generalized modified $k$-Bessel function

TL;DR

This paper develops solutions for a broad class of fractional kinetic equations involving the generalized modified k-Bessel function, which can model anomalous reactions in chaotic dynamical systems.

Contribution

It introduces a general framework for solving fractional kinetic equations with the generalized modified k-Bessel function, encompassing many known and new solutions.

Findings

Derived explicit solutions for fractional kinetic equations with generalized modified k-Bessel functions.

Unified approach applicable to various special cases and related functions.

Potential applications in modeling anomalous reactions in chaotic systems.

Abstract

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions for various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations associated with the generalized modified $k$-Bessel function of the first kind. It is also pointed out that the main results presented here are general enough to be able to be specialized to yield many known and (presumably) new solutions for fractional kinetic equations.