Caputo-Katugampola type Implicit fractional differential equation with two-point anti-periodic boundary conditions

Abstract

The given article describes the implicit fractional differential equation with anti-periodic boundary conditions in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the given problem and prove the existence and uniqueness results of such a problem using the Banach and Krasnoselskii Fixed point theorems. Further, by applying generalized Gronwall inequality, the Ulam-Hyers stability results are discussed. To show the eectiveness of the acquired results, convenient examples are presented.