@article{article_974148, title={Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions}, journal={Results in Nonlinear Analysis}, volume={5}, pages={12–28}, year={2022}, DOI={10.53006/rna.974148}, author={Redhwan, Saleh and Shaikh, Sadikali and Abdo, Mohammed}, keywords={implicit fractional differential equation, fractional derivative and fractional integral, anti-periodic conditions, fixed point theorem, Gronwall inequality}, abstract={The given article describes the implicit fractional dierential equation with anti-periodic boundary conditions <br />in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the <br />given problem and prove the existence and uniqueness results of such a problem using the Banach and <br />Krasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, the Ulam-Hyers <br />stability results are discussed. To show the eectiveness of the acquired results, convenient examples are <br />presented.}, number={1}, publisher={Erdal KARAPINAR}