@article{Kalsoom2023, 
author = {Amna Kalsoom and Sehar Afsheen and Akbar Azam and Faryad Ali},
title = {Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {7766-7786},
keywords = {fractional differential equation, boundary value problem, positive solution, fractional Green's function, fixed-point theorem},
url = {https://www.sciopen.com/article/10.3934/math.2023390},
doi = {10.3934/math.2023390},
abstract = {In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.}
}