On Hilfer-Prabhakar fractional derivatives Sawi transform and its applications to fractional differential equations

Abstract

The goal of this paper is to study the Sawi transform and its relationship to Hilfer-Prabhakar and regularized Hilfer-Prabhakar fractional derivatives, as well as to present some lemmas related to the Sawi transform. Additionally, the paper aims to find solutions for Cauchy type fractional differential equations using Hilfer-Prabhakar fractional derivatives, by utilizing the Sawi and Fourier transforms, and involving the threeparameter Mittag-Leffler function.

New generalized integral transform on Hilfer-Prabhakar fractional derivatives and its applications

“…s and ϕ(s) = 1 s 2 , the new generalized integral transform will result in the Sawi transform to the regularized Hilfer-Prabhakar fractional derivative, which was studied in a recent paper available on arXiv.org [30]. If the Sawi transform of z(t) is denoted by R(s)…”

“…Mahgoub et al [17] found new integral transform called as Sawi transform, this transform has a deeper connection with Laplace, Elzaki, Sumudu,Shehu, Kamal and Monand transform. In our earlier paper available on arXiv.org [30], we applied the Sawi transform on Hilfer-Prabhakar derivative and their regularization versions to applied these results on some Cauchy type fractional differential equations.…”