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Generalized Fractional Integral Operators Involving Mittag‐Leffler Function

Author

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  • Hafte Amsalu
  • D. L. Suthar

Abstract

The aim of this paper is to study various properties of Mittag‐Leffler (M‐L) function. Here we establish two theorems which give the image of this M‐L function under the generalized fractional integral operators involving Fox’s H‐function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and K‐transforms are also presented. On account of general nature of M‐L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

Suggested Citation

  • Hafte Amsalu & D. L. Suthar, 2018. "Generalized Fractional Integral Operators Involving Mittag‐Leffler Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:7034124
    DOI: 10.1155/2018/7034124
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    References listed on IDEAS

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    1. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    2. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Sunil Chandak & Anita Alaria & Biniyam Shimelis, 2022. "Composition Formula for Saigo Fractional Integral Operator Associated with V‐Function," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. D. L. Suthar & Hafte Amsalu, 2019. "Fractional Integral and Derivative Formulas by Using Marichev‐Saigo‐Maeda Operators Involving the S‐Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    3. S. Chandak & Biniyam Shimelis & Nigussie Abeye & A. Padma, 2021. "The Marichev‐Saigo‐Maeda Fractional Calculus Operators Pertaining to the V‐Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    4. 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, John Wiley & Sons, vol. 2019(1).
    5. D. L. Suthar & Teklay Hailay, 2020. "Euler‐Type Integral Operator Involving S‐Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).

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