On the Solution of Distributional Abel Integral Equation by Distributional Sumudu Transform

This section deals with the definition, terminologies, and properties of the Sumudu transform and the Abel integral equation. In Section 2, solution of Abel integral equation is obtained by the application of the Sumudu transform, and in Section 3, the Sumudu transform is proved for distribution spaces, and the solution of Abel integral equation in the sense of distribution is obtained. The Sumudu transform is introduced by Watugala 1, 2 to solve certain engineering problems. Complex inversion formula for the Sumudu transform is given by Weerakoon 3 . For more of its applications, see 4–6 . Let M be a constant and τ1 and τ2 need not exist simultaneously each may be infinite . Then, the set A is defined by