Solution of Partial and Integro-Differential Equations Using the Convolution of Ramadan Group Transform
Mohamed A. Ramadan *
Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt.
Asmaa K. Mesrega
Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Differential and integral as well as Partial integro-differential equations (PIDE) occur naturally in various fields of science, engineering and social sciences. In this article, the Ramadan group integral transform of the convolution is used to solve such types of equations. We propose a most general form of a linear PIDE with a convolution kernel. First, the PIDE is converted to an ordinary differential equation (ODE) using Ramadan group transform (RGT). Solving this ordinary differential equation and applying inverse RGT an exact solution of the problem is obtained. Illustrative examples are considered to demonstrate the applicability and the effectiveness of the proposed RG transform of convolution for solving integral and integro- differential equations. It is observed that the RGT is a simple, more general and reliable technique for solving such equations.
Keywords: Partial and integro-differential equations, the convolution of Ramadan Group transform, Ramadan Group transform