On solution of fractional kinetic equation involving Riemann xi function via Sumudu transform

Abstract

Several significant questions of mathematics and mathematical physics have been effectively explained and answered through the use of fractional kinetic equations containing special functions. Due to the high importance of arbitrary-order kinetic equations, the aim of this work is to obtain the solution of a new arbitrary-order kinetic equation related to the Riemann xi function. The Sumudu transform technique is used to solve it. The findings are plotted with the help of MATLAB R2016a. The outcomes of the paper are in the form of an infinite series representation of the Riemann xi function and in terms of the Mittag-Leffler function.