Fixed point approach to solve nonlinear fractional differential equations in orthogonal F " role="presentation"> F F \mathcal{F} -metric spaces

[摘要] In this paper, we introduce the notion of a generalized ($ \alpha $, $ \Theta _{\mathcal{F}}) $-contraction in the context of an orthogonal $ \mathcal{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.

[学科分类] 地球科学(综合)

[关键词] orthogonal set;orthogonal $ \mathcal{F} $-metric space;generalized $ (\alpha;\Theta _{\mathcal{F}}) $-contraction;fixed point;nonlinear fractional differential equation