Open Access

ARTICLE

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Nawab Hussain^1,*, Saud M. Alsulami¹, Hind Alamri^1,2,*
1 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
2 Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia
* Corresponding Authors: Nawab Hussain. Email: ; Hind Alamri. Email:
(This article belongs to this Special Issue: Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2617-2648. https://doi.org/10.32604/cmes.2023.023143

Received 10 May 2022; Accepted 14 July 2022; Issue published 23 November 2022

Abstract

In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results.

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Keywords

Common fixed points; Reich and Chatterjea mappings; Krasnoselskii-Ishikawa iteration; complete metric space; Banach space; integral equation; nonlinear fractional differential equation

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