Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Terms of the Green's Function and the AC-Laplace Transform
Tohru Morita *
Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan.
Ken-ichi Sato
College of Engineering, Nihon University, Koriyama 963-8642, Japan.
*Author to whom correspondence should be addressed.
Abstract
The particular solutions of inhomogeneous differential equations with polynomial coefficients in terms of the Green's function are obtained in the framework of the AC-Laplace transform, that is the Laplace transform supplemented by its analytic continuation. In particular, discussions are given on Kummer's and the hypergeometric differential equation, and also on a fractional differential equation with coefficients of polynomial of at most first degree.
Keywords: Green's function, AC-Laplace transform, particular solution, Kummer's Differential equation, hypergeometric Differential equation, fractional Differential equation