Complex order fractional differential equation in complex domain with mixed boundary condition

Abstract

Fractional calculus of complex orders in the complex domain is a rapidly growing field of interest among many mathematicians. While fractional differential equations in real variables have received much attention recently, attempts to solve such equations in complex variables have been rather scant. This research work deals with the complex order fractional differential equation with boundary conditions. The existence of solutions is established by using Dhage’s fixed point theorem with some conditions, whereas the application of the Banach contraction principle obtains the uniqueness of the solution. Moreover, Ulam–Hyers stability of the considered problem is also discussed in this work. Examples and application are presented to verify the obtained results.