Uniqueness of solutions and Ulam–Hyers–Mittag-Leffler stability for Hammerstein-type Hilfer delay differential equations of fractional order

Nonlinear Engineering 2026 Open access

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Authors: Cemil Tunҫ, Bashir Ahmad, Osman Tun
DOI: 10.1515/nleng-2025-0200
Cited by: 1
References: 36

Abstract

Abstract In this paper, we discuss the existence of a unique solution and Ulam–Hyers–Mittag-Leffler (UHML) stability for a nonlinear Hammerstein-type ψ -Hilfer delay differential equation of fractional order ( ψ -HFDDE) in the configuration of several variable time-dependent delays. Our study is based on fixed-point methodology. The results established in this work are novel and enhance the literature on the topic. We also present examples to illustrate the application of the obtained results. The findings of this paper provide new contributions to the qualitative theory of Hilfer fractional delay differential equations.

Fields of Study & Subjects

Nonlinear Differential Equations Analysis Fractional Differential Equations Solutions Fuzzy Systems and Optimization

Publication details

Journal / source
Nonlinear Engineering
Publisher
Walter de Gruyter GmbH
Volume
15
Issue
1
Publication date
1 January 2026
Language
EN