Solving a Nonlinear Fractional Differential Equation Using Fixed Point Results in Orthogonal Metric Spaces

Abstract

This research article aims to solve a nonlinear fractional differential equation by fixed point theorems in orthogonal metric spaces. To achieve our goal, we define an orthogonal Θ-contraction and orthogonal (α,Θ)-contraction in the setting of complete orthogonal metric spaces and prove fixed point theorems for such contractions. In this way, we consolidate and amend innumerable celebrated results in fixed point theory. We provide a non-trivial example to show the legitimacy of the established results.

Keywords

• nonlinear fractional differential equation
• fixed point
• orthogonal (α
• Θ)-contraction
• orthogonal metric space