Solution of fractional differential equation by fixed point results in orthogonal F-metric spaces

Abstract

In this paper, we solve the existence and uniqueness of a solution for a fractional differential equation by introducing some new fixed point results for rational ($ \alpha $, $ \beta $, $ \psi $)-contractions in the framework of orthogonal $ \mathcal{F} $-metric spaces. We derive some well-known results in literature as consequences of our leading result.

Keywords

• fixed point
• orthogonal $ \mathcal{f} $-metric space
• orthogonal cyclic ($ \alpha
• \; \beta) $-admissible
• rational ($ \alpha $
• $ \beta
• \; \psi $)-contraction
• fractional differential equations