Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

Abstract

The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function to introduce the $(p,q;l)$-extended $τ$-Gauss hypergeometric and the $(p,q;l)$-extended $τ$-confluent hypergeometric functions with some of their properties, such as the Laplace-type and the Euler-type integral formulas. Another is to apply them to fractional kinetic equations that appear in astrophysics and physics using the Laplace transform method.