부산대학교 도서관

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 ψ(s)ϕ(s) and ψ(s)ϕ(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.