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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fuli He & Ahmed Bakhet & Muajebah Hidan & Hala Abd-Elmageed, 2022. "ON THE CONSTRUCTION OF (p,k)-HYPERGEOMETRIC FUNCTION AND APPLICATIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-8, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402617
    DOI: 10.1142/S0218348X22402617
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