Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions

Authors : Saleh REDHWAN, Sadikali SHAİKH, Mohammed ABDO

Pages : 12-28

Doi:10.53006/rna.974148

View : 19 | Download : 5

Publication Date : 2022-03-31

Article Type : Research Paper

Abstract :The given article describes the implicit fractional dierential 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 xed 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.
Keywords : implicit fractional differential equation, fractional derivative and fractional integral, anti periodic conditions, fixed point theorem, Gronwall inequality