The operational solution of fractional-order differential equations, as well as Black–Scholes and heat-conduction equations

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• 作者：K. V. Zhukovsky
• 刊名：Moscow University Physics Bulletin
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：71
• 期：3
• 页码：237-244
• 全文大小：814 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-8460
• 卷排序：71

文摘

Operational solutions to fractional-order ordinary differential equations and to partial differential equations of the Black–Scholes and of Fourier heat conduction type are presented. Inverse differential operators, integral transforms, and generalized forms of Hermite and Laguerre polynomials with several variables and indices are used for their solution. Examples of the solution of ordinary differential equations and extended forms of the Fourier, Schrödinger, Black–Scholes, etc. type partial differential equations using the operational method are given. Equations that contain the Laguerre derivative are considered. The application of the operational method for the solution of a number of physical problems connected with charge dynamics in the framework of quantum mechanics and heat propagation is demonstrated.Keywordsinverse operatorSchrödinger equationBlack–Scholes equationheat conductionLaguerre and Hermite polynomials