ON THE CONSTRUCTION OF (p,k)-HYPERGEOMETRIC FUNCTION AND APPLICATIONS

Fuli He, Ahmed Bakhet (), Muajebah Hidan () and Hala Abd-Elmageed ()
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Fuli He: School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China
Ahmed Bakhet: Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
Muajebah Hidan: Department of Mathematics, Faculty of Science for King Khalid University, Abha 61471, Saudi Arabia
Hala Abd-Elmageed: Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-8

Abstract: In this paper, we construct a (p,k)-hypergeometric function by using the Hadamard product, which we call the generalized (p,k)-hypergeometric function. Several properties, namely, convergence properties, derivative formulas, integral representations and differential equations are indicated of this function. The latter function is a generalization of the usual hypergeometric function, the k-analogue of hypergeometric function and other hypergeometric functions are recently presented. As an application, we obtain the solution of the generalized fractional kinetic equations involving of the generalized (p,k)-hypergeometric function.

Keywords: Hypergeometric Functions; Integral Formulas; Fractional Differential Equations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402617

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