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Operational method of solution of linear non-integer ordinary and partial differential equations

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the oper...

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Detalles Bibliográficos
Autor principal: Zhukovsky, K. V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4747974/
https://www.ncbi.nlm.nih.gov/pubmed/26900541
http://dx.doi.org/10.1186/s40064-016-1734-3
Descripción
Sumario:We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black–Scholes-like equations etc. are demonstrated by the operational technique.