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On Novel Fractional Integral and Differential Operators and Their Properties

Author

Listed:
  • Shahid Mubeen
  • Rana Safdar Ali
  • Yasser Elmasry
  • Ebenezer Bonyah
  • Artion Kashuri
  • Gauhar Rahman
  • Çetin Yildiz
  • A. Hussain

Abstract

The main goal of this paper is to describe the new version of extended Bessel–Maitland function and discuss its special cases. Then, using the aforementioned function as their kernels, we develop the generalized fractional integral and differential operators. The convergence and boundedness of the newly operators and compare them with the existing operators such as the Saigo and Riemann–Liouville fractional operators are explored. The integral transforms of newly defined and generalized fractional operators in terms of the generalized Fox–Wright function are presented. Additionally, we discuss a few exceptional cases of the main result.

Suggested Citation

  • Shahid Mubeen & Rana Safdar Ali & Yasser Elmasry & Ebenezer Bonyah & Artion Kashuri & Gauhar Rahman & Çetin Yildiz & A. Hussain, 2023. "On Novel Fractional Integral and Differential Operators and Their Properties," Journal of Mathematics, Hindawi, vol. 2023, pages 1-20, May.
    • Handle: RePEc:hin:jjmath:4165363
    DOI: 10.1155/2023/4165363
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