On Properties of ά -Sumudu Transform and Applications

Abstract

The α-Sumudu transform is defined and its properties are proved. α-Sumudu transform of convolution product and composition of functions is obtained. The α-Sumudu transform of Riemann-Liouville integral and derivatives of fractional order are determined. As an application, the solution of Initial Value Problems with Riemann-Liouville derivative of fractional order is obtained. .