Qualitative analysis of implicit Dirichlet boundary value problem for Caputo-Fabrizio fractional differential equations

Abstract

This article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch's and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results. Copyright © 2020 Rozi Gul et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.