@article{Al-Mazrooei2023, 
author = {Abdullah Eqal Al-Mazrooei and Jamshaid Ahmad},
title = {Fixed point approach to solve nonlinear fractional differential equations in orthogonal        F  -metric spaces},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {5080-5098},
keywords = {fixed point, orthogonal set, orthogonal F-metric space, nonlinear fractional differential equation, generalized (α, ΘF)-contraction},
url = {https://www.sciopen.com/article/10.3934/math.2023255},
doi = {10.3934/math.2023255},
abstract = {In this paper, we introduce the notion of a generalized (   α,        Θ                  F              )-contraction in the context of an orthogonal        F  -complete metric space and obtain some new fixed point results for this newly introduced contraction. A nontrivial example is also provided to satisfy the validity of the established results. As consequences of our obtained results, we derive the leading results in [Fixed Point Theory Appl., 2015,185, 2015] and [Symmetry, 2020, 12,832]. As an application, we investigate the existence and uniqueness of the solution for a nonlinear fractional differential equation.}
}