Stability results for fractional integral pantograph differential equations involving two Caputo operators-Reference-Cited by-同舟云学术

Stability results for fractional integral pantograph differential equations involving two Caputo operators

Published:2022 Issue:3 Volume:8 Page:6009-6025
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Moumen Abdelkader¹,Shafqat Ramsha²,Hammouch Zakia³,Niazi Azmat Ullah Khan²,Jeelani Mdi Begum¹

Affiliation:

1. Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia

2. Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan

3. Department of Sciences, Ecole normale superieure, Moulay Ismail University, Morocco

Abstract

<abstract><p>In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutions to a fractional-order pantograph differential equation (FOPDE) with two Caputo operators. Banach's fixed point (BFP) and Leray-alternative Schauder's are used to prove the existence- uniqueness of solutions. In addition, we discuss and demonstrate various types of Ulam-stability for our problem. Finally, an example is provided for clarity.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference37 articles.

1. A. A. Alderremy, K. M. Saad, P. Agarwal, S. Aly, S. Jain, Certain new models of the multi space-fractional Gardner equation, Phys. A: Stat. Mech. Appl., 545 (2020), 123806. https://doi.org/10.1016/j.physa.2019.123806

2. R. Caponetto, G. Dongola, L. Fortuna, I. Petráš, Fractional order systems: modeling and control applications, Vol. 72, Singapore: World Scientific, 2010. https://doi.org/10.1142/7709

3. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Vol. 204, Elsevier, 2006.

4. R. Almeida, N. R. O. Bastos, M. T. T. Monteiro, Modeling some real phenomena by fractional differential equations, Math. Methods Appl. Sci., 39 (2016), 4846–4855. https://doi.org/10.1002/mma.3818

5. J. Wang, Y. Yang, W. Wei, Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces, Opusc. Math., 30 (2010), 361–381. https://doi.org/10.7494/OpMath.2010.30.3.361

Cited by 3 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. Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system;Results in Physics;2023-08

2. Controllability of fractional stochastic evolution inclusion via Hilfer derivative of fixed point theory;AIMS Mathematics;2023

3. Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability;AIMS Mathematics;2023