A faster iterative scheme for solving nonlinear fractional differential equations of the Caputo type-Reference-Cited by-同舟云学术

A faster iterative scheme for solving nonlinear fractional differential equations of the Caputo type

Published:2023 Issue:12 Volume:8 Page:28488-28516
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Okeke Godwin Amechi¹,Udo Akanimo Victor¹,Alqahtani Rubayyi T.²,Alharthi Nadiyah Hussain²

Affiliation:

1. Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria

2. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

Abstract

<abstract><p>In this paper, we introduce a new fixed point iterative scheme called the AG iterative scheme that is used to approximate the fixed point of a contraction mapping in a uniformly convex Banach space. The iterative scheme is used to prove some convergence result. The stability of the new scheme is shown. Furthermore, weak convergence of Suzuki's generalized non-expansive mapping satisfying condition (C) is shown. The rate of convergence result is proved and it is demonstrated via an illustrative example which shows that our iterative scheme converges faster than the Picard, Mann, Noor, Picard-Mann, M and Thakur iterative schemes. Data dependence results for the iterative scheme are shown. Finally, our result is used to approximate the solution of a nonlinear fractional differential equation of Caputo type.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference44 articles.

1. A. Atangana, D. Baleanu, Application of fixed point theorem for stability analysis of a nonlinear Schrodinger with Caputo-Liouville derivative, Filomat, 31 (2017), 2243–2248. https://doi.org/10.2298/FIL1708243A

2. E. Karapinar, T. Abdeljawad, F. Jarad, Applying new fixed point theorems on fractional and ordinary differential equations, Adv. Differ. Equ., 2019 (2019), 421. https://doi.org/10.1186/s13662-019-2354-3

3. G. A. Okeke, D. Francis, C. A. Nse, A generalized contraction mapping applied in solving modified implicit $\phi$-Hilfer pantograph fractional differential equations, J. Anal., 31 (2023), 1143–1173.

4. M. Syam, M. Al-Refai, Fractional differential equations with Atangana–Baleanu fractional derivative: Analysis and applications, Chaos Soliton. Fract. X, 2 (2019), 100013. https://doi.org/10.1016/j.csfx.2019.100013

5. X. Zhang, P. Chen, Y. Wu, B. Wiwatanapataphee, A necessary and sufficient condition for the existence of entire large solutions to a $k$-Hessian system, Appl. Math. Lett., 145 (2023), 108745. https://doi.org/10.1016/j.aml.2023.108745

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions;AIMS Mathematics;2024