Computable solution of fractional kinetic equations using Mathieu-type series

Abstract

The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several diverse ways. In this line, our aim is to study the solution of fractional kinetic equations involving generalized Mathieu-type series. The generality of this series will help us to deduce results related to a fractional kinetic equation involving another form of Mathieu series. To obtain the solution, we use the Laplace transform technique. Besides, a graphical representation is given to observe the behavior of the obtained solutions.

Solution of Fractional Kinetic Equations Associated with the p,q-Mathieu-Type Series

“…We leave those to the interested reader as an exercise. Moreover, if we set p � q � 0 and τ � ω in our main results, then we arrive at [4]. In this article, we considered the traditional kinetic equation as a recent fractional generalization and proposed their solutions.…”

“…e complex conditions program at a basic stem of differential equations, which illustrates the amount of modification of a star's chemical composition with each configuration in terms of generation and annihilation reaction levels. e expansion and sweeping statement of fractional kinetic equations related with different special functions were established (see [1][2][3][4][5][6][7][8][9][10][11] for details). Nowadays, several scholars are developing a simplified structure of the fractional kinetic equation involving the Mathieu-type series to make the dynamic state extremely relevant and acceptable in a few astrophysical problems.…”

Stability analysis of distributed order of Hilfer nonlinear systems

“…More recently, we can find works that address the fractional derivative of Hilfer 26,27 as well as multiple interesting applications in various fields of science, for instance, in engineering, physics, and economics, with other types of fractional derivatives such as Caputo and Caputo‐Frabizio 28‐49 …”

Existence and multiplicity of solutions for fractional Schödinger equation involving a critical nonlinearity

“…Recently, fractional calculus attained more importance due to its wide applications in various field, such as diffusion, electrical circuits, control theory, blood flow phenomena, electro-analytical chemistry, etc. ; for details, see [1][2][3][4][5][6][7][8][9][10][11][12] and the references therein. Problem (1.1) is related to the standing wave solutions of the following fractional nonlinear Schödinger equation of the form:…”