Convergence Analysis of a New Implicit Iterative Scheme and Its Application to Delay Caputo Fractional Differential Equations.
- Resource Type
- Article
- Authors
- Ofem, Austine Efut; Udo, Mfon Okon; Joseph, Oboyi; George, Reny; Chikwe, Chukwuka Fernando
- Source
- Fractal & Fractional. Mar2023, Vol. 7 Issue 3, p212. 21p.
- Subject
- *DELAY differential equations
*FRACTIONAL differential equations
*BANACH spaces
- Language
- ISSN
- 2504-3110
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. [ABSTRACT FROM AUTHOR]