Operational Methods For Sub - Ballistic And Coupled Fractional PDEs

Abstract

In this article, it is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve a certain system of fractional PDEs and a variety of Lamb - Bateman singular integral equation. The Lamb - Bateman singular integral equation was introduced to study the solitary wave diffraction. It may be concluded that the integral transforms and exponential operators are effective methods for solving integral equations and fractional linear equations with non-constant coefficients.