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

DOI10.1016/j.jmaa.2016.08.054zbMath1364.35016OpenAlexW2518073295MaRDI QIDQ321814

K. V. Zhukovskiĭ

Publication date: 14 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.08.054

zbMATH Keywords

inverse operatorhyperbolic heat equationBlack-ScholesHermite and Laguerre polynomialsLaguerre derivative operator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Other special methods applied to PDEs (35A25) Fractional ordinary differential equations (34A08) Fokker-Planck equations (35Q84)

Related Items (10)

Periodic solution for second-order impulsive differential inclusions with relativistic operator ⋮ Theoretical Analysis of the Radiation Properties of Some Major X‐Ray Free Electron Lasers ⋮ Exact analytic solution and investigation of the Guyer-Krumhansl heat equation ⋮ Periodic boundary layer solutions of a reaction-diffusion problem with singularly perturbed boundary conditions of the third kind ⋮ Fourier two-temperature model to describe ultrafast laser pulses interaction with metals: a novel mathematical technique ⋮ Solving evolutionary-type differential equations and physical problems using the operator method ⋮ Some applications of Wright functions in fractional differential equations ⋮ Exact solutions to the fractional differential equations with mixed partial derivatives ⋮ Some exact solutions to non-Fourier heat equations with substantial derivative ⋮ EXACT RESULTS ON SOME NONLINEAR LAGUERRE-TYPE DIFFUSION EQUATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Evolution of non-spreading Airy wavepackets in time dependent linear potentials
• Orthogonality properties of the Hermite and related polynomials
• Operational methods and differential equations with applications to initial-value problems
• Operational formulas connected with two generalizations of Hermite polynomials
• A representation theory for solutions of a higher order heat equation. I
• A representation theory for solutions of a higher order heat equation. II
• Integral transforms in science and engineering
• Generalized polynomials, operational identities and their applications
• Analytical solutions for heat diffusion beyond Fourier law
• A new family of integral transforms and their applications
• Operational methods, special polynomial and functions and solution of partial differential equations
• On Crofton-Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case

This page was built for publication: Operational solution for some types of second order differential equations and for relevant physical problems