{"title":"Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses","authors":"Surendra Kumar, Paras Sharma","doi":"10.1007/s13540-025-00415-3","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"129 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-025-00415-3","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.