Existence and stability results of pantograph equation with three sequential fractional derivatives-Reference-Cited by-同舟云学术

Existence and stability results of pantograph equation with three sequential fractional derivatives

Published:2022 Issue:3 Volume:8 Page:5216-5232
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Houas Mohamed¹,Kaushik Kirti²,Kumar Anoop²,Khan Aziz³,Abdeljawad Thabet³⁴

Affiliation:

1. Laboratory FIMA, UDBKM, Khemis Miliana University, Algeria

2. Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India

3. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

4. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Sufficient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference33 articles.

1. M. Ahmad, J. Jiang, A. Zada, Z. Ali, Z. Fu, J. Xu, Hyers-Ulam-Mittag-Leffler stability for a system of fractional neutral differential equations, Discrete Dyn. Nat. Soc., 2020 (2020), 2786041. https://doi.org/10.1155/2020/2786041

2. I. Ahmad, J. J. Nieto, G. U. Rahman, K. Shah, Existence and stability for fractional order pantograph equations with nonlocal conditions, Electron. J. Differ. Equ., 132 (2020), 1–16.

3. G. Ali, K. Shah, G. ur Rahman, Investigating a class of pantograph differential equations under multi-points boundary conditions with fractional order, Int. J. Appl. Comput. Math., 7 (2021), 2. https://doi.org/10.1007/s40819-020-00932-0

4. K. Balachandran, S. Kiruthika, J. J. Trujillo, Existence of solutions of nonlinear fractional pantograph equations, Acta Math. Sci., 33 (2013), 712–720. https://doi.org/10.1016/S0252-9602(13)60032-6

5. A. Granas, J. Dugundji, Fixed point theory, New York: Springer-Verlag, 2003. https://doi.org/10.1007/978-0-387-21593-8

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