title: Operational method of solution of linear non-integer ordinary and partial differential equations.
abstract: 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.
authors.affiliation: Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia 119991.
authors.forename: K V
authors.initials: KV
authors.lastname: Zhukovsky
keywords: Derivative; Differential equation; Hermite and Laguerre polynomials; Inverse operator; Special functions