Operational solution for some types of second order differential equations and for relevant physical problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Zhukovsky, K. V.¹ 

[1] Moscow MV Lomonosov State Univ, Fac Phys, Moscow 119991, Russia

关键词: Inverse operator;    Differential equation;    Fokker-Planck equation;    Hyperbolic heat equation;    Hermite and Laguerre polynomials;   

DOI  :  10.1016/j.jmaa.2016.08.054

来源: Elsevier

【 摘 要 】

We present an operational method to obtain solutions for differential equations, describing a broad range of physical problems, including ordinary non-integer order and high order partial differential equations. Inverse differential operators are proposed to solve a variety of differential equations. Integral transforms and the operational exponent are used to obtain the solutions. Generalized families of orthogonal polynomials and special functions are also employed with recourse to their operational definitions. Examples of solutions of physical problems, related to propagation of the heat and other quantities are demonstrated by the developed operational technique. In particular, the evolution type problems, the generalizations of the Black Scholes, of the heat conduction, of the Fokker Planck equations are considered as well as equations, involving the Laguerre derivative operator. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free