Abstract

In this research, we present necessary and sufficient conditions for the existence and uniqueness of positive solutions for a class of Hilfer–Hadamard-type fractional differential equations with boundary value problems, including those with integral boundary conditions. The obtained results are conditional on a specific set of strong assumptions, which substantially narrow the class of admissible nonlinearities, coefficients, and boundary data. Thus, the present work extends the Hadamard-type framework to the Hilfer–Hadamard setting only within this restrictive regime, rather than providing a full extension to all Hilfer–Hadamard systems. We utilize the properties of (Formula presented.) -concave and sub-homogeneous operators along with two Banach fixed point theorems to achieve our results. An illustrative example is also provided to demonstrate the applicability of the methodology and highlight the main findings. The novelty of our work in this paper is twofold: First, we have expanded the scope by considering Hilfer–Hadamard-type fractional differential equations. Second, we employed a new fixed point theorem to improve our results within this particular framework.

Department(s)

Mathematics and Statistics

Publication Status

Open Access

Keywords and Phrases

Green function; Hilfer–Hadamard-type fractional differential equation; positive solution; γ-concave and sub-homogeneous operator

International Standard Serial Number (ISSN)

2504-3110

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2026 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jul 2026

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