Fixed point approach to solve nonlinear fractional differential equations in orthogonal $\mathcal{F}$-metric spaces

In this paper, we introduce the notion of a generalized ( $\alpha$, ${\mathrm{\Theta }}_{\mathcal{F}})$-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.