Existence results and Ulam stability for some problem of fractional differential equations

Abstract

The objective of this work is to study the existence and uniqueness of the solution to a problem involving the generalized Mittag-Leffler fractional derivative, and to a mixed hybrid problem that includes first kind fractional derivatives in the senses of Riemann and Caputo, within the framework of the p-Laplace operator. The stability of the solution has been examined according to the concept of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability. The existence and uniqueness results are established by applying fixed point theorems such as those of Banach, Krasnoselskii, and Schaefer.