@article{Guedim2025, 
author = {Souad Guedim and Amar Benkerrouche and Mohammed Said Souid and Abdelkader Amara and Rashid Jan and Imtiaz Ahmad},
title = {Initial value problem for fractional differential equations of variable order},
year = {2025},
journal = {Mathematical Modelling and Control},
volume = {5},
number = {4},
pages = {379-389},
keywords = {existence and uniqueness of solutions, initial value problem, fractional variable order, uniform stability, fixed point theorem},
url = {https://www.sciopen.com/article/10.3934/mmc.2025026},
doi = {10.3934/mmc.2025026},
abstract = {This study presented a novel approach to investigating the existence, uniqueness, and stability of solutions for an initial value problem involving fractional differential equations of variable order. In contrast to conventional methods in the literature, which often utilized generalized intervals and piecewise constant functions, we introduced a new fractional operator that is more appropriate for this problem. The existence and uniqueness of the solutions ware demonstrated through Leray-Schauder fixed point theorem and Banach's theorem, with an analysis of the uniform stability of the problem. The strength of our approach lies in its straightforwardness and reliance on fewer restrictive assumptions. The study concluded with an application that features a practical example, accompanied by visual illustrations.}
}