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Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application

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  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawser 11991, Saudi Arabia)

Abstract

A generalized form of the Mittag-Leffler function denoted by p E q ; δ λ , μ ; ν x is established and studied in this paper. The fractional integrals involving the newly defined function are investigated. As an application, the solutions of a generalized fractional kinetic equation containing this function are derived and the nature of the solution is studied with the help of graphical analysis.

Suggested Citation

  • Kottakkaran Sooppy Nisar, 2019. "Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1230-:d:297126
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    References listed on IDEAS

    as
    1. Saxena, R.K. & Mathai, A.M. & Haubold, H.J., 2004. "On generalized fractional kinetic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 657-664.
    2. J. A. Tenreiro Machado & Alexandra M. S. F. Galhano & Juan J. Trujillo, 2014. "On development of fractional calculus during the last fifty years," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 577-582, January.
    3. Jean-Daniel Djida & Gisèle Mophou & Iván Area, 2019. "Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 540-557, August.
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