Approximation of the Solution of Delay Fractional Differential Equation Using <i>AA</i>-Iterative Scheme

Abstract

The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.

Keywords

• <i>AA</i>-iterative scheme
• fixed point
• delay fractional differential equations
• enriched contraction
• enriched nonexpansive mapping