Qualitative analysis of multi-term fractional differential equations involving psi-Caputo derivative

Abstract

The aim of the reported results in this manuscript is to handle the existence, uniqueness and Ulam-Hyers stability of solutions for a novel form of multi-term fractional differential equations associated with two different fractional orders in the $\psi$--Caputo sense. The existence, uniqueness, and stability in the sense of Ulam are established for the suggested system. Our prospective is rely on the $\psi$--Caputo's derivatives and implementation of Krasnoselskii's and Banach contraction with respect to the Bielecki norm to obtain the uniqueness of solution on a bounded domain in a Banach space. Finally, we discuss the Ulam-Hyers stability criteria for the main fractional system. As applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems.