Recently, a new deformation of the Sumudu transforms namely, conformable Sumudu transform has been introduced. In this article, we generalize the concept of one-dimensional conformable Sumudu transform into two-dimensional conformable Sumudu transform namely, conformable double Sumudu transform. Further, we present and prove some main properties and theorems related to the introduced transform. In order to illustrate the validity, efficiency, and applicability of the proposed transform, we apply the conformable double Sumudu transform to solve initial and boundary value problems of conformable fractional partial differential equations.

In this study, we employ fuzzy Sumudu transform to find the solution for system of linear fuzzy differential equations where the system possesses fuzzy constant coeffcients instead of crisp. For this purpose, fuzzy Sumudu transform has been revisited and a brief comparison with fuzzy Laplace transform is provided alongside, particularly on the scale preserving property. For the sake of comparison, we introduce to the literature a time scaling theorem for fuzzy Laplace transform. Next, the system with fuzzy constant coeffcients is interpreted under the strongly generalized differentiability. From here, new procedures for solving the systems are proposed. A numerical example is then carried out for solving a system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

In this paper, we discuss the existence of double Sumudu transform and study relationships between Laplace and Sumudu transforms. Further, we apply two transforms to solve linear ordinary differential equations with constant coefficients and non constant coefficients.

A new generalized Laplace transform is introduced, which is a common generalization of the Laplace transform, Sumudu transform, ELzaki transform, and a transformation of X. J. Yang. The basic properties of this generalized Laplace transform are derived, so that these properties coincide with the properties of the known transformations mentioned above.