A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques

Abstract

In this paper, we introduce the notion of orthogonal α–F–convex contraction mapping and prove some fixed-point theorems for self-mapping in orthogonal complete metric spaces. The proven results generalize and extend some of the well-known results in the literature. Following the derivation of these fixed-point results, we propose a solution for the fractional integro-differential equation, utilizing the fixed-point technique within the context of orthogonal complete metric spaces.

Keywords

• orthogonal set
• orthogonal complete metric space
• orthogonal continuous
• orthogonal preserving
• orthogonally α-admissible
• fixed point