- Results in Nonlinear Analysis
- Vol: 5 Issue: 1
- Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary condit...
Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions
Authors : Saleh Redhwan, Sadikali Shaikh, Mohammed Abdo
Pages : 12-28
Doi:10.53006/rna.974148
View : 15 | Download : 7
Publication Date : 2022-03-31
Article Type : Research
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