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Research Article | Open Access

Existence and uniqueness of the solution to Caputo-Hadamard differential equations with delay and nonlocal conditions

Nguyen Hoang Tuan1,2, Vo Viet Tri3( )
Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet, District 10, Ward 14, Ho Chi Minh City, Vietnam
Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City
Division of Applied Mathematics, Thu Dau Mot University, 06 Tran Van On, Binh Duong Province, Vietnam
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Abstract

In this paper, we established the existence conditions for initial value problems involving the Caputo-Hadamard derivative operator with delay and nonlocal conditions. The problems were analyzed for various source functions. In a special case, we obtained a unique solution. These results were derived by combining the concept of the measure of non-compactness with appropriate applications of fixed point theorems. Additionally, we provided illustrative examples to support the theoretical findings.

Keywords

Caputo-Hadamard derivativefractional differentialfractional equationmeasurenoncompactness
CLC number: 35R11, 26A33, 35B44, 34A08, 26A33

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Communications in Analysis and Mechanics
Volume 17 Issue 3,
September 2025
Pages 725-748
DOI: 10.3934/cam.2025029

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Cite this article:
Tuan NH, Tri VV. Existence and uniqueness of the solution to Caputo-Hadamard differential equations with delay and nonlocal conditions. Communications in Analysis and Mechanics, 2025, 17(3): 725-748. https://doi.org/10.3934/cam.2025029

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Received: 10 December 2024
Revised: 07 April 2025
Accepted: 17 July 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)