{"title":"Group classification of time fractional Black-Scholes equation with time-dependent coefficients","authors":"Jicheng Yu, Yuqiang Feng","doi":"10.1007/s13540-024-00339-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present Lie symmetry analysis for time fractional Black-Scholes equation with time-dependent coefficients. The group classification is carried out by investigating the time-dependent coefficients <span>\\(\\sigma (t)\\)</span>, <i>r</i>(<i>t</i>) and <i>s</i>(<i>t</i>). Then the obtained group generators are used to reduce the equation under study, some of the reduced equations are fractional ordinary equations with Erdélyi-Kober fractional derivative, and some exact solutions including power series solutions are constructed.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-09-16","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/s13540-024-00339-4","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
In this paper, we present Lie symmetry analysis for time fractional Black-Scholes equation with time-dependent coefficients. The group classification is carried out by investigating the time-dependent coefficients \(\sigma (t)\), r(t) and s(t). Then the obtained group generators are used to reduce the equation under study, some of the reduced equations are fractional ordinary equations with Erdélyi-Kober fractional derivative, and some exact solutions including power series solutions are constructed.
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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