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On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus

Author

Listed:
  • Ahmed Bakhet

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt)

  • Abd-Allah Hyder

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
    Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 11371, Egypt)

  • Areej A. Almoneef

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mohamed Niyaz

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt)

  • Ahmed H. Soliman

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt)

Abstract

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hypergeometric matrix function and state some integral equations and differential formulas about it. Next, we obtain some results about fractional calculus of these extended incomplete Wright hypergeometric matrix functions. Finally, we discuss an application of the extended incomplete Wright hypergeometric matrix function in the kinetic equations.

Suggested Citation

  • Ahmed Bakhet & Abd-Allah Hyder & Areej A. Almoneef & Mohamed Niyaz & Ahmed H. Soliman, 2022. "On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4371-:d:978571
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    References listed on IDEAS

    as
    1. Chaojun Zou & Mimi Yu & Ahmed Bakhet & Fuli He & Eric Campos-Canton, 2021. "On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions," Complexity, Hindawi, vol. 2021, pages 1-8, December.
    2. Haile Habenom & D. L. Suthar & Melaku Gebeyehu, 2019. "Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué Type Struve Function," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-8, June.
    3. D. L. Suthar & S. D. Purohit & Serkan Araci, 2020. "Solution of Fractional Kinetic Equations Associated with the - Mathieu-Type Series," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-7, August.
    4. Dumitru Baleanu & Praveen Agarwal, 2014. "On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
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