Integral Transforms of the Hilfer-Type Fractional Derivatives

Abstract

In this paper, some important properties concerning the Hilfer-type fractional derivative are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform, Mellin transform and Fourier transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus. An application is get with the Jafari transform and nite Hankel transform to obtain the analytical solution to fractional radial diffusion equation in terms of the \(\kappa\)-Hilfer fractional derivative.