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.