Xie Mengqi, Khan Sami Ullah, Sumelka Wojciech, Alamri Atif M, AlQahtani Salman A
Department of Electronic Information Engineering, Xi'an Technological University, Xi'an, 710021, China.
Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, 2500, Pakistan.
Sci Rep. 2024 May 27;14(1):12047. doi: 10.1038/s41598-024-62851-0.
In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.
近年来，由于分数阶微积分能够对具有不确定性和记忆效应的复杂现象进行建模，将其纳入随机延迟系统的研究兴趣日益浓厚。分数阶随机延迟微分方程在围绕各种应用领域对这类复杂动力系统进行建模方面很常见。本研究提出了一种新颖的谱方法，以证明具有分数阶导数和时间延迟的随机系统的稳定性行为和数值解。通过弥合分数阶微积分、随机过程和谱分析之间的差距，这项工作为分数动力学领域做出了贡献，并丰富了可用于研究具有延迟和不确定性系统稳定性的分析工具库。为了说明我们方法的实际意义并验证理论结果，给出了一些数值模拟。
