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

Abstract

In this paper, we obtain the new generalized integral transform on Prabhakar integral, Hilfer-Prabhakar derivatives and regularized Hilfer-Prabhakar fractional derivatives. Next, we evaluate the solution of some Cauchy type fractional differential equation with Hilfer-Prabhakar fractional derivatives by applying the new integral transform and Fourier transforms which involves three parameter Mittage-Leffler function.

Exploring the Elzaki Transform: Unveiling Solutions to Reaction-Diffusion Equations with Generalized Composite Fractional Derivatives

“…The fractional RDE has numerous applications, ranging from biology, and chemistry to physics and economics. They provide a valuable tool for modeling anomalous diffusion, subdiffusion, superdiffusion, and long-range interactions, as opposed to standard integer-order RDE [1][2][3]. Fractional derivatives are non-local and non-linear, making fractional RDE challenging to solve.…”

Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

“…The HP fractional derivative (HPFD) and its regularized Caputo version were introduced in [6]. Panchal et al [7] computed the Sumudu integral transform of HP fractional derivatives and demonstrated its applications to Cauchy problems. Moreover, Singh et al [8] provided the solution for a free-electron laser (FEL) equation modeled with the HP fractional order derivative using the Elzaki transform.…”