Convergence Analysis of a New Implicit Iterative Scheme and Its Application to Delay Caputo Fractional Differential Equations-Reference-Cited by-同舟云学术

Convergence Analysis of a New Implicit Iterative Scheme and Its Application to Delay Caputo Fractional Differential Equations

Published:2023-02-24 Issue:3 Volume:7 Page:212
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Ofem Austine Efut¹^ORCID,Udo Mfon Okon²,Joseph Oboyi³^ORCID,George Reny⁴^ORCID,Chikwe Chukwuka Fernando³

Affiliation:

1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South Africa

2. Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin P.M. Box 1167, Nigeria

3. Department of Mathematics, University of Calabar, Calabar P.M. Box 1115, Nigeria

4. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Abstract

This article presents a new three-step implicit iterative method. The proposed method is used to approximate the fixed points of a certain class of pseudocontractive-type operators. Additionally, the strong convergence results of the new iterative procedure are derived. Some examples are constructed to authenticate the assumptions in our main result. At the end, we use our new method to solve a fractional delay differential equation in the sense of Caputo. Our main results improve and generalize the results of many prominent authors in the existing literature.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/3/212/pdf

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