Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses

IF 2.5 2区 数学 Q1 MATHEMATICS
Surendra Kumar, Paras Sharma
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引用次数: 0

Abstract

The current study discusses the approximate solutions for a class of fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses (NIIs) defined on a separable Hilbert space. The approximation to the nonlinear functions is obtained using orthogonal projection operator. The existence and convergence of the sequence of approximate solutions is proved using a fixed point theorem and analytic semigroup theory. Moreover, we show that finite-dimensional approximations converge, guaranteeing both computational feasibility and theoretical soundness. This study emphasises on short-memory systems, which are very significant for modelling fading memory effects. We demonstrate the practical importance and versatility of our method by applying it on fractional stochastic Burgers’ and subdiffusion equations.

非瞬时脉冲驱动的短记忆分数阶随机积分微分方程的近似解
本文讨论了在可分离Hilbert空间上由非瞬时脉冲驱动的一类具有短记忆的分数阶随机积分微分方程的近似解。利用正交投影算子得到了非线性函数的近似。利用不动点定理和解析半群理论证明了近似解序列的存在性和收敛性。此外,我们证明了有限维近似收敛,保证了计算可行性和理论合理性。本研究的重点是短时记忆系统,这对于模拟记忆衰退效应非常重要。通过将该方法应用于分数阶随机Burgers方程和次扩散方程,我们证明了该方法的实用性和通用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Fractional Calculus and Applied Analysis
Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
4.70
自引率
16.70%
发文量
101
期刊介绍: Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
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