Fixed point approach to solve nonlinear fractional differential equations in orthogonal F-metric spaces

Abstract

In this paper, we introduce the notion of a generalized (α, ΘF)-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.

Keywords

• orthogonal set
• orthogonal f-metric space
• generalized (α，θf)-contraction
• fixed point
• nonlinear fractional differential equation