INVESTIGATION OF THE PERIODICITY AND STABILITY OF SOLUTIONS FOR CERTAIN DELAY FUNCTIONAL NEUTRAL DIFFERENTIAL SYSTEMS

Anis Bouhnik, Ahcene Djoudi (), Abdelouaheb Ardjouni (), Rashid Jan, Ibrahim Mekawy () and Taha Radwan
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Anis Bouhnik: Department of Mathematics, Faculty of Sciences, University of Annaba, P. O. Box 12, Annaba 23000, Algeria2Department of Mathematics, University of Souk Ahras, P. O. Box 1553, Souk Ahras 41000, Algeria
Ahcene Djoudi: Applied Mathematics Lab, Department of Mathematics, Faculty of Sciences, University of Annaba, P. O. Box 12, Annaba 23000, Algeria
Abdelouaheb Ardjouni: Department of Mathematics, University of Souk Ahras, P. O. Box 1553, Souk Ahras 41000, Algeria
Rashid Jan: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering Universiti Tenaga Nasional (UNITEN), Kajang, Selangor, Malaysia5Department of Mathematics, Saveetha School of Engineering (SIMATS), Thandalam 600124, Chennai, Tamil Nadu, India
Ibrahim Mekawy: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Taha Radwan: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-20

Abstract: This study investigates the stability and existence of periodic solutions in neutral differential systems with time delays and variable coefficients. By utilizing Krasnoselskii’s fixed point theorem, we demonstrate a set of sufficient conditions ensuring the existences of such a periodic solution. This involves transforming the system into an equivalent integral form before applying the fundamental matrix solutions alongside Floquet theory. In addition, we will analyze the asymptotic stability of these solutions, thus establishing new conditions that can ensure stability. The practical relevance of our theoretical results is supported through numerical examples, validating the proposed approach, and highlighting its suitability in areas such as electrical circuits, control systems, and biological modeling. This study extends previous work and thereby offers a detailed framework intended for use in studying neutral differential systems where time delays are present.

Keywords: Mathematical Model; Neutral Differential Systems; Periodic Solutions; Asymptotic Stability; Fixed Point Method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401760

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