@article{Samadi2024, 
author = {Ayub Samadi and Chaiyod Kamthorncharoen and Sotiris K. Ntouyas and Jessada Tariboon},
title = {Mixed Erdélyi-Kober and Caputo fractional differential equations with nonlocal non-separated boundary conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {32904-32920},
keywords = {existence and uniqueness, Caputo fractional derivative, Erdélyi-Kober fractional derivative, fixed point theorems, nonlocal boundary conditions},
url = {https://www.sciopen.com/article/10.3934/math.20241574},
doi = {10.3934/math.20241574},
abstract = {In this paper, we investigate a sequential fractional boundary value problem that contains a combination of Erdélyi-Kober and Caputo fractional derivative operators subject to nonlocal, non-separated boundary conditions. We establish the uniqueness of the solution by using Banach's fixed point theorem, while via Krasnosel'skiĭ's fixed-point theorem and Leray-Schauder's nonlinear alternative, we prove the existence results. The obtained results are illustrated by constructed numerical examples.}
}