On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the $\psi$-Hilfer operator

We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the $\psi$-Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions. A few examples are presented in order to illustrate the possible applications of our main results.