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Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions

  • Muthaiah Subramanian ORCID logo , Murugesan Manigandan , Akbar Zada ORCID logo EMAIL logo and Thangaraj Nandha Gopal
Published/Copyright: October 27, 2022

Abstract

In this paper, we analyses the existence and Hyers–Ulam stability of a coupled system of three sequential fractional differential equations with coupled integral boundary conditions. This manuscript can be categorized into three parts: The Leray–Schauder alternative is used to prove the existence of a solution in the first section. The second section emphasizes the analysis of uniqueness, which is based on the Banach fixed point theorem’s concept of contraction mapping, and the third section establishes the Hyers–Ulam stability results. In addition, we provide examples to demonstrate our findings.

2010 MSC: 34A08; 34B15; 45G15

Corresponding author: Akbar Zada, Department of Mathematics, University of Peshawar, Peshawar, Pakistan, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2022-04-12
Accepted: 2022-09-29
Published Online: 2022-10-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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