Dynamic k-Struve Sumudu solutions for fractional kinetic equations

Kottakkaran Sooppy Nisar,Fethi Bin Muhammad Belgacem

doi:10.1186/s13662-017-1397-6

Abstract

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

Highlights

The Struve function Hν(x) introduced by Hermann Struve in, defined for ν ∈ C by ∞ (– )r x r+ν+ Hν(x) := r= (r + / ) (r + ν ) ( )
The Sumudu transform was introduced by Watugala
Corollary By putting k = in Theorem, we get the solution of fractional kinetic equation involving classical

Summary

Introduction

The Struve function Hν(x) introduced by Hermann Struve in , defined for ν ∈ C by. is the particular solutions of the non-homogeneous Bessel differential equations, given by x y (x) + xy (x) +. Is the particular solutions of the non-homogeneous Bessel differential equations, given by x y (x) + xy (x) +. For more details about Struve functions, their generalizations and properties, the esteemed reader is invited to consider the references [ – ]. Nisar et al [ ] introduced and studied various properties of k-Struve function Skν,c defined by. The Sumudu transform was introduced by Watugala (see [ , ]). For more details about the Sumudu transform, see ([ , – ]). The Sumudu transform over the set of functions. We use the Sumudu transform technique to obtain the solutions of fractional kinetic equations by considering ( ). The applications of fractional order calculus are found in many papers (see [ – ]), and it has attracted researchers’ attention in various fields [ – ] because of its importance and efficiency. The fractional differential equation between a chemical reaction or a production scheme (such as in birthdeath processes) was established and treated by Haubold and Mathai [ ] ( see [ , , ])

Solution of generalized fractional kinetic equations for k-Struve function

Conclusion