Integral Transforms of the Hilfer-Type Fractional Derivatives
F. S. Costa *
Aerospace Engineering, Departament of Mathematics, UEMA, Brazil.
J. C. A. Soares
Department of Mathematics, UNEMAT, Brazil.
S. Jarosz
Department of Applied Mathematics, Imecc-Unicamp, Brazil.
J. Vanterler da C. Sousa
Aerospace Engineering, Departament of Mathematics, UEMA, Brazil.
*Author to whom correspondence should be addressed.
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.
Keywords: Jafari transform, Fundamental theorem of fractional calculus, Hilfer-Type fractional derivative, \(\kappa\)-Riesz fractional derivative and time-fractional radial diffusion