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Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution

Author

Listed:
  • Serkan Araci

    (Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey)

  • Gauhar Rahman

    (Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir 18000, Pakistan)

  • Abdul Ghaffar

    (Department of Mathematical Science, BUITEMS, Quetta 87300, Pakistan)

  • Azeema

    (Department of Mathematics, SBK Women University, Quetta 87300, Pakistan)

  • Kottakkaran Sooppy Nisar

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

Abstract

Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. Finally, we derive some of the particular cases of the main results.

Suggested Citation

  • Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:248-:d:212589
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    References listed on IDEAS

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    5. Saiful R. Mondal & K. S. Nisar, 2014. "Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, April.
    6. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, April.
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    Cited by:

    1. Gauhar Rahman & Abdus Saboor & Zunaira Anjum & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "An Extension of the Mittag‐Leffler Function and Its Associated Properties," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    2. Pallavi Sharma & Ekta Mittal & D. L. Suthar & Rajni Gupta, 2025. "Some New Application of Extended Wright Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).

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