@article{Suebcharoen2023, 
author = {Teeranush Suebcharoen and Watchareepan Atiponrat and Khuanchanok Chaichana},
title = {Fixed point theorems via auxiliary functions with applications to two-term fractional differential equations with nonlocal boundary conditions},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {7394-7418},
keywords = {contraction, fixed point, two-term fractional differential equation},
url = {https://www.sciopen.com/article/10.3934/math.2023372},
doi = {10.3934/math.2023372},
abstract = {In this study, the    (  h-   φ      )    R   and    (  h-   φ      )    M  -contractions with two metrics endowed with a directed graph are examined using auxiliary functions. We propose a set of criteria that guarantees the existence of common fixed points for our contractions. This leads to a generalization of previous results in the literature. Towards our accomplishments, we establish affirmative results that demonstrate solutions to a class of nonlinear two-term fractional differential equations with nonlocal boundary conditions. To further corroborate our major findings, we also provide instances.}
}