Abstract
Solution of the Abel integral equation is obtained using the Sumudu transform and further, distributional Sumudu transform, and, distributional Abel equation are established.
Highlights
This section deals with the definition, terminologies, and properties of the Sumudu transform and the Abel integral equation
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
Summary
This section deals with the definition, terminologies, and properties of the Sumudu transform and the Abel integral equation. The Sumudu transform of nth order derivative of f t is defined by. Fn u denotes the Sumudu transform of nth antiderivative of f t , which is obtained by integrating the function f t n times successively, that is. Let f t and g t be continuous functions defined for t ≥ 0, possessing Sumudu transforms F u and G u , respectively. If f is of exponential order, its Sumudu transform F u exists, which is given by f t e− t/u dt, 1.11 where 1/u 1/η i/τ. The defining integral for F exists at point 1/u 1/η i/τ in the right hand plane η > K and ζ > L. The solution can be obtained by two methods which are shown in 7, pages 44-45
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