@article{Abdellouahab2025, 
author = {Naimi Abdellouahab and Keltum Bouhali and Loay Alkhalifa and Khaled Zennir},
title = {Existence and stability analysis of a problem of the Caputo fractional derivative with mixed conditions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6805-6826},
keywords = {fractional derivative, existence, Ulam-stability, mixed conditions, iterative methods},
url = {https://www.sciopen.com/article/10.3934/math.2025312},
doi = {10.3934/math.2025312},
abstract = {Recently, initial-boundary-value problems with the Caputo fractional derivative for ordinary differential equations have been intensively studied. This paper studies a nonlinear integro-differential equation of fractional order, containing a composition of fractional derivatives with different origins and mixed conditions. The equation under consideration acts as a model equation of motion in a fractal medium. First, we use three fixed-point theorems to prove the existence and uniqueness results. Then, the Ulam stability criterion of the solution is given. The main results will be illustrated by a proposed example.}
}