2024 : 6 : 13
Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review
Type
JournalPaper
Keywords
fractional calculus; fractional stochastic partial differential equations; numerical method; finite difference method; finite element method; Fourier spectral method
Year
2024
Journal Symmetry
DOI
Researchers Behrouz Parsa Moghaddam ، Afshin Babaei ، Arman Dabiri ، Alexandra Galhano

Abstract

This article aims to provide a comprehensive review of the latest advancements in numerical methods and practical implementations in the field of fractional stochastic partial differential equations (FSPDEs). This type of equation integrates fractional calculus, stochastic processes, and differential equations to model complex dynamical systems characterized by memory and randomness. It introduces the foundational concepts and definitions essential for understanding FSPDEs, followed by a comprehensive review of the diverse numerical methods and analytical techniques developed to tackle these equations. Then, this article highlights the significant expansion in numerical methods, such as spectral and finite element methods, aimed at solving FSPDEs, underscoring their potential for innovative applications across various disciplines.