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

TL;DR

This paper explores the Sawi transform's connection to Hilfer-Prabhakar fractional derivatives and applies these concepts to solve fractional differential equations using transforms and special functions.

Contribution

It introduces new relationships between the Sawi transform and Hilfer-Prabhakar derivatives and demonstrates their application in solving fractional differential equations.

Findings

Established lemmas for the Sawi transform.

Derived solutions for fractional differential equations.

Connected Sawi transform with Mittag-Leffler functions.

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 three-parameter Mittag-Leffler function.