Approximation of the Solution of Delay Fractional Differential Equation Using AA -Iterative Scheme

Mujahid Abbas, Muhammad Waseem Asghar and Manuel De la Sen
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Mujahid Abbas: Department of Mathematics, Government College University, Lahore 54000, Pakistan
Muhammad Waseem Asghar: Department of Mathematics, Government College University, Lahore 54000, Pakistan
Manuel De la Sen: Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain

Mathematics, 2022, vol. 10, issue 2, 1-20

Abstract: The aim of this paper is to propose a new faster iterative scheme (called A A -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 A A -iterative scheme.

Keywords: AA -iterative scheme; fixed point; delay fractional differential equations; enriched contraction; enriched nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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