Solutions of Fractional Kinetic Equations using the (?, ?; ?)-Extended ?- Gauss Hypergeometric Function

Solutions of Fractional Kinetic Equations using the (?, ?; ?)-Extended ?- Gauss Hypergeometric Function

The main objective of this paper is to use the newly proposed (?, ?; ℓ)-extended beta function to introduce the (?, ?; ℓ)-extended ?-Gauss hypergeometric and the (?, ?; ℓ)-extended ?- 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.

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