A Method of Inverse Differential Operators Using Ortogonal Polynomials and Special Functions for Solving Some Types of Differential Equations and Physical Problems

A general operational method, which is based on the developed technique of the inverse derivative operator, for solving a wide range of problems described by some classes of differential equations is represented. The inverse derivative operators for solving a number of differential equations are constructed and used. The operational identities are derived with the use of the inverse derivative operator, integral transformations, and generalized forms of orthogonal polynomials and special functions. Examples of solving various partial differential equations, such as equations of heat conduction and diffusion, as well as the Fokker-Planck equation, etc. are given. The application of the operational approach to solving a number of physical problems, among them problems related to the motion of charged particles in external field, is demonstrated.