Fractional boundary value problem in complex domain

Abstract

Fractional calculus of complex order in complex domain has emerged as a brand-new area of study. Over the past few years, fractional boundary value problems (FBVP) in real variables have been extensively studied but there are few attempts on these types of problems in complex variables. In this study, the existence and uniqueness for the solutions of fractional differential equation (FDE) in complex domain with boundary conditions is examined. We established the existence of solutions using the Krasnoselskii fixed point theorem; however, the uniqueness result is proved by applying the Banach contraction principle. To explain our findings, an illustrative example is presented. The special cases of the derived findings are equivalent to the theorems that already exist.