Integral Transforms of the Hilfer-Type Fractional Derivatives

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, Mellintransform and Fourier transform. These integral transforms are used to derive a fractional version of thefundamental theorem of calculus. An application is get with the Jafari transform and finite Hankel transformto obtain the analytical solution to fractional radial diffusion equation in terms of the κ-Hilfer fractionalderivative.