On some existence results for nonlinear fractional differential equations with hybrid proportional Caputo derivatives

Fatima Ezzahra Bourhim; Prof. Ali  El Mfadel; M'hamed Elomari

doi:10.5269/bspm.67782

Authors

Fatima Ezzahra Bourhim Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, 23000, Beni Mellal, Morocco
Prof. Ali El Mfadel
M'hamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

DOI:

https://doi.org/10.5269/bspm.67782

Abstract

The purpose of this manuscript is to establish the existence and uniqueness of some solutions to a class of boundary value problems for a generalized nonlinear hybrid Caputo fractional differential equation with nonlocal boundary conditions. The proofs of our main results are derived from mixed Lipshitz and Caratheodory conditions and some basic techniques of $\Psi$-fractional calculus. Some fundamental $\Psi$-fractional differential inequalities are also established. As an application, an nontrivial example is given in the last part of this paper to illustrate our theoretical results.