In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numerical example is provided to illustrate the usage of the FST.

The main aim of this paper is to propose a novel method for finding the solutions of fuzzy partial differential equations (FPDEs) through fuzzy Sumudu transform. For this purpose, two new theorems for FST regarding fuzzy partial derivatives will be introduced. To demonstrate the effectiveness of the method, a numerical example will be provided. Finally, this paper opens up a new research direction on FPDEs.