A study of fractional differential equations with proportional boundary conditions

Ahmed Alsaedi; Rabab Alghamdi; Bashir Ahmad; Sotiris K. Ntouyas

doi:10.2478/auom-2026-0002

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A study of fractional differential equations with proportional boundary conditions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 34 (2026): Issue 1 (May 2026)

By: Ahmed Alsaedi, Rabab Alghamdi, Bashir Ahmad and Sotiris K. Ntouyas

Open Access

|May 2026

Abstract

This article deals with a new concept of nonlocal proportional segmental boundary conditions with respect to initial and terminal sections of the given domain. Equipped with these conditions, we investigate the existence and uniqueness of solutions for a Caputo-type fractional differential equation with the nonlinearity depending upon the unknown function together with its lower order fractional derivative. We apply the standard tools of the fixed point theory to accomplish the desired results. Our study is useful in the given configuration as it helps to comprehend the fractional boundary value problems in the sense of proportional boundary conditions.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2026-0002 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 29 - 51

Submitted on: Aug 6, 2025

Accepted on: Nov 15, 2025

Published on: May 15, 2026

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Caputo fractional derivative,

proportional boundary conditions,

Related subjects:

© 2026 Ahmed Alsaedi, Rabab Alghamdi, Bashir Ahmad, Sotiris K. Ntouyas, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 34 (2026): Issue 1 (May 2026)