Work

Initial Value Problem for Mixed Differential Equations of Variable Order with Finite Delay

Year: 2025

Type: article

Abstract: This study presents a fresh perspective on the existence, uniqueness, and stability of solutions for initial value problems involving variable-order differential equations with finite delay. Departing from conventional techniques that utilize generalized intervals and piecewise constant functions, we introduce a novel fractional operator tailored for this specific problem. Our methodology integrates sophisticated mathematical analysis, including the Schauder fixed-point theorem and Banach’s contraction principle, with an examination of the Ulam–Hyers stability of the problem. The strength of our approach is in its simplicity, requiring fewer restrictive assumptions. We conclude with a practical application to illustrate our findings. These results are valuable for understanding complex dynamical systems with time delays, offering applications in diverse fields such as engineering, economics, and medicine, and enhancing numerical methods for solving delay equations.

Source: Symmetry

DOI: 10.3390/sym17020295

Authors: Souad Guedim, Amar Benkerrouche, Kanokwan Sitthithakerngkiet, Mohammed Said Souid, Abdelkader Amara

Institutions: University of Ouargla, Ziane Achour University of Djelfa, King Mongkut's University of Technology North Bangkok, Université IBN Khaldoun Tiaret

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: King Mongkut's University of Technology North Bangkok