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On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator

Author

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  • Yanyan Zhang
  • Ghulam Farid
  • Zabidin Salleh
  • Ayyaz Ahmad

Abstract

The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fractional integral operator is constructed.

Suggested Citation

  • Yanyan Zhang & Ghulam Farid & Zabidin Salleh & Ayyaz Ahmad, 2021. "On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:6043769
    DOI: 10.1155/2021/6043769
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