@article{Alghamdi2024, 
author = {Najla Alghamdi and Bashir Ahmad and Esraa Abed Alharbi and Wafa Shammakh},
title = {Investigation of multi-term delay fractional differential equations with integro-multipoint boundary conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12964-12981},
keywords = {delay differential equations, stability criteria, nonlocal integral boundary conditions, Caputo fractional drivative},
url = {https://www.sciopen.com/article/10.3934/math.2024632},
doi = {10.3934/math.2024632},
abstract = {A new class of nonlocal boundary value problems consisting of multi-term delay fractional differential equations and multipoint-integral boundary conditions is studied in this paper. We derive a more general form of the solution for the given problem by applying a fractional integral operator of an arbitrary order        β          ξ       instead of        β          1      ; for details, see Lemma 2. The given problem is converted into an equivalent fixed-point problem to apply the tools of fixed-point theory. The existence of solutions for the given problem is established through the use of a nonlinear alternative of the Leray-Schauder theorem, while the uniqueness of its solutions is shown with the aid of Banach's fixed-point theorem. We also discuss the stability criteria, icluding Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias, and generalized Ulam-Hyers-Rassias stability, for solutions of the problem at hand. For illustration of the abstract results, we present examples. Our results are new and useful for the discipline of multi-term fractional differential equations related to hydrodynamics. The paper concludes with some interesting observations.}
}