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On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function

Author

Listed:
  • Muhammad Samraiz

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Ahsan Mehmood

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Saima Naheed

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Gauhar Rahman

    (Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan)

  • Artion Kashuri

    (Department of Mathematics, Faculty of Technical and Natural Sciences, University Ismail Qemali, 9400 Vlora, Albania)

  • Kamsing Nonlaopon

    (Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional operators, such as the semi-group and inverse characteristics, are studied. As special cases of these novel fractional operators, several fractional operators that are already well known in the literature are acquired. The generalized Laplace transform of these operators is evaluated. By involving the explored fractional operators, a kinetic differintegral equation is introduced, and its solution is obtained by using the Laplace transform. As a real-life problem, a growth model is developed and its graph is sketched.

Suggested Citation

  • Muhammad Samraiz & Ahsan Mehmood & Saima Naheed & Gauhar Rahman & Artion Kashuri & Kamsing Nonlaopon, 2022. "On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function," Mathematics, MDPI, vol. 10(21), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3991-:d:955325
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    References listed on IDEAS

    as
    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Zhao, Dazhi & Luo, Maokang, 2019. "Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 531-544.
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