Work

Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ -Laplacian operator

Year: 2026

Type: article

Abstract: In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ -Laplacian operator and subject to fractional integral boundary conditions. Building upon recent existence results for this class of equations, we establish sufficient conditions under which solutions exhibit Ulam–Hyers stability. The analysis relies on nonlinear analysis techniques and properties of the μ -Laplacian operator. Two illustrative examples are provided: one for classical Ulam–Hyers stability and another for uniform stability under a variable perturbation described by a power-type control function.

Source: Open Mathematics

DOI: 10.1515/math-2025-0296

Authors: Kadda Maazouz, Abderrahmane Ouardani, Rabah Bechayeb, Abdelkader Moumen, Mohamed Bouye

Institutions: Université IBN Khaldoun Tiaret, University of Ha'il, King Khalid University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,187

OpenAlex ID: W7223208303

FWCI:

Cites: 17

Cited by:

Related to: 10