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

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Tarih

2024

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Universal Wiser Publisher

Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

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.

Açıklama

Anahtar Kelimeler

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

Kaynak

Contemporary Mathematics

WoS Q Değeri

N/A

Scopus Q Değeri

Q4

Cilt

5

Sayı

3

Künye