Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola type

Abstract

This paper deals with a nonlinear implicit fractional differential equation with the anti-periodic boundary condition involving the Caputo-Katugampola type. The existence and uniqueness results are established by applying the fixed point theorems of Krasnoselskii and Banach. Further, by using generalized Gronwall inequality the Ulam-Hyers stability results are proved. To demonstrate the effectiveness of the main results, appropriate examples are granted.

Keywords

• fractional differential equations
• katugampola fractional operator
• ulam-hyers stability
• fixed point theorems
• fractional gronwall inequality