Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives-Reference-Cited by-同舟云学术

Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

Published:2023 Issue:3 Volume:8 Page:6913-6941
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Hammad Hasanen A.¹²,Aydi Hassen³⁴⁵,Işık Hüseyin⁶,De la Sen Manuel⁷

Affiliation:

1. Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

3. Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia

4. China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

6. Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma 10200, Balıkesir, Turkey

7. Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), Spain

Abstract

<abstract><p>The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference48 articles.

1. K. Diethelm, A. D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, Scientific Computing in Chemical Engineering Ⅱ-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, Springer-Verlag, Heidelberg, 1999,217–224.

2. L. Gaul, P. Klein, S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Pr., 5, (1991), 81–88. https://doi.org/10.1016/0888-3270(91)90016-X

3. W. G. Glockle, T. F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J., 68 (1995), 46–53. https://doi.org/10.1016/S0006-3495(95)80157-8

4. R. Hilfer, Applications of fractional calculus in physics, World Scientific, Singapore, 2000.

5. F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien, (1997) 291–348.

Cited by 23 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. Existence and Stability of Solutions for p-Proportional ω-Weighted κ-Hilfer Fractional Differential Inclusions in the Presence of Non-Instantaneous Impulses in Banach Spaces;Fractal and Fractional;2024-08-14

2. Fixed Point Methodologies for ψ-Contraction Mappings in Cone Metric Spaces over Banach Algebra with Supportive Applications;International Journal of Analysis and Applications;2024-07-19

3. Solving Fractional Random Differential Equations by Using Fixed Point Methodologies under Mild Boundary Conditions;Fractal and Fractional;2024-06-28

4. Existence and stability results for a Langevin system with Caputo–Hadamard fractional operators;International Journal of Geometric Methods in Modern Physics;2024-06-12

5. Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives;Chaos, Solitons & Fractals;2024-05