Qualitative Analysis of Delay Stochastic Systems with Generalized Memory Effects

Abdelhamid Mohammed Djaouti () and Muhammad Imran Liaqat
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Abdelhamid Mohammed Djaouti: Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia
Muhammad Imran Liaqat: Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan

Mathematics, 2025, vol. 13, issue 21, 1-31

Abstract: Fractional stochastic differential equations (FSDEs) are powerful tools for modeling real-world phenomena, as they incorporate both memory effects and stochastic noise. A central focus in their analysis is establishing the well-posedness and regularity of solutions. Moreover, the averaging principle offers a systematic approach to simplify complex dynamical systems by approximating their behavior through time-averaged models. In this paper, we develop a theoretical framework for a class of FSDEs involving the Hilfer–Katugampola derivative. Our main contributions include proving the well-posedness and regularity of solutions, establishing a generalized averaging principle, and demonstrating real-life applications solved via the Euler–Maruyama method. All numerical simulations were conducted using the Python programming language (version 3.11). These results are formulated for the P ˜ th moment, providing a unified analysis that extends existing findings.

Keywords: generalized fractional derivative; qualitative theory; Jensen’s inequality; averaged system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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