Fractional Frontier: Navigating Cauchy-Type Equations with Formable and Fourier Transformations

Authors

  • Mohd Khalid Department of Mathematics, Maulana Azad National Urdu University, Gachibowli, Hyderabad, India
  • Ali Akgül Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, Turkey

DOI:

https://doi.org/10.37256/cm.5320244620

Keywords:

Prabhakar integral, Hilfer-Prabhakar derivatives, formable transform, Fourier transform, Mittag-Leffler function

Abstract

The Formable integral transform for the Hilfer-Prabhakar and Prabhakar fractional derivatives, as well as their regularised forms, are derived in this article. We solve several Cauchy-type fractional differential equations with Hilfer-Prabhakar fractional derivatives by applying the Formable integral and Fourier transformations in their entirety, including the three-parameter Mittag-Leffler function. With the help of analytical solutions and improved comprehension of complicated fractional differential equations, this work expands the use of integral transforms in fractional calculus across a range of scientific and engineering fields.

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Published

2024-07-30

How to Cite

1.
Khalid M, Akgül A. Fractional Frontier: Navigating Cauchy-Type Equations with Formable and Fourier Transformations. Contemp. Math. [Internet]. 2024 Jul. 30 [cited 2024 Dec. 11];5(3):2693-708. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4620

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