Investigation of a class of differential equations of complex order with boundary conditions

In this manuscript, a class of boundary value problems (BVPs) of complex order fractional differential equations (COFDEs) using the Caputo–Fabrizio (C–F) operator is considered. We develop appropriate results for the existence and uniqueness of solution to the problem under our study using Banach and Krasnoselskii’s fixed-point theorem. In addition, some others tools of nonlinear analysis are utilized in the derivation of our results. Additionally, we also derive some necessary conditions for stability analysis of the proposed problem using the concept of Ulam and Hyers (U–H). Finally, an example to justify our theoretical findings is given.