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

In this paper, we obtain the new generalized integral transform of the Prabhakar integral, Prabhakar derivative, and Hilfer-Prabhakar fractional derivatives. Using these results, we obtained several existing results for different integral transforms by varying the unknown functions psi(s) and psi(s). Next, using Hilfer-Prabhakar derivatives, a three-parameter Mittage-Leffler function (MLF), a contemporary integral transform, and a Fourier transform, we evaluate the solutions to a few fractional differential equations of the Cauchy-type.