@article{Aljurbua2024, 
author = {Saleh Fahad Aljurbua},
title = {Extended existence results for FDEs with nonlocal conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9049-9058},
keywords = {fractional derivatives, differential equations, fractional differential equations, existence of solutions, fixed-point theorem},
url = {https://www.sciopen.com/article/10.3934/math.2024440},
doi = {10.3934/math.2024440},
abstract = {This paper discusses the existence of solutions for fractional differential equations with nonlocal boundary conditions (NFDEs) under essential assumptions. The boundary conditions incorporate a point    0  ≤  c  <  d and fixed points at the end of the interval    [  0  ,  d  ]. For    i  =  0  ,  1, the boundary conditions are as follows:         a          i        ,      b          i        >  0,        a          0        p  (  c  )  =  −      b          0        p  (  d  )  ,        a          1            p                          ′              (  c  )  =  −      b          1            p                          ′              (  d  ). Furthermore, the research aims to expand the usability and comprehension of these results to encompass not just NFDEs but also classical fractional differential equations (FDEs) by using the Krasnoselskii fixed-point theorem and the contraction principle to improve the completeness and usefulness of the results in a wider context of fractional differential equations. We offer examples to demonstrate the results we have achieved.}
}