A Modern Approach To Fractional-Order Kinetic Equations With Hyper-Bessel Function Solutions And Application On Environmental Field

Abstract

This study presents a novel approach to solving fractional-order kinetic equations (FKEs) by employing Hyper-Bessel functions in conjunction with the Sumudu transform. The proposed method leverages the Sumudu transform to obtain analytical solutions of FKEs, wherein the function f(t) is expressed in terms of a Hyper-Bessel function. The resulting solutions are general in nature and can be applied to a wide range of existing as well as newly formulated fractional kinetic equations, with potential applications in environmental science and related fields.Special functions included in fractional kinetic equations have been shown to be helpful in the explanation and resolution of numerous important mathematical and mathematical physics issues. Because arbitrary-order kinetic equations are so important, the goal of this study is to use the Sumudu Transform technique to solve a new fractional-order kinetic equation involving the Hyper Bessel function with their fractional derivatives. MATLAB-generated graphical representations used in our analysis to demonstrate the behavior of these solutions under various parametric values. The outcomes of the study are highly flexible and may lead to both confirmed and maybe undiscovered research findings in this field.