In this paper, we propose a new approximate method, namely homotopy analysis Sumudu transform method (HASTM) to solve various linear and nonlinear Fokker-Planck equations.The homotopy analysis Sumudu transform method is a combined form of the Sumudu transform method and the homotopy analysis method. The proposed technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results obtained by the proposed method show that the approach is very efficient, simple and can be applied to other nonlinear problems.

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.

This paper investigates the semi-analytical solutions of linear and non-linear Time Fractional Klein-Gordon equations with appropriate initial conditions to apply the New Sumudu-Adomian Decomposition method (NSADM). This paper shows the semi-analytical as well as a graphical interpretation of the solution by using mathematical software “, Mathematica Wolform”,and considering Caputo’, s sense derivatives to semi-analytical results obtained by NSADM.