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 Sum...

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.

The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current number existing transforms such those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties prove some important results, including linearity property, existence theorem, convolution derivatives properties. Moreover, pro...

Recently, Shehu has introduced an integral transform called transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In literature, many transforms were used to compute solution of integro-differential equations (IDEs). this article, for first time, we use computation $n^{\text{th}}$-order IDEs. We present a general scheme give some examples with ...

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional S...