Applications of the Fuzzy Sumudu Transform for the Solution of First Order Fuzzy Differential Equations

Abstract

Abstract: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.

Fuzzy Sumudu Transform for Solving System of Linear Fuzzy Differential Equations with Fuzzy Constant Coefficients

“…Recently, Ahmad and Abdul Rahman [13,14], proposed fuzzy Sumudu transform (FST) for solving FDEs with fuzzy initial values which was done under the strongly generalized differentiability concept. The authors successfully introduced some of FST fundamental properties and theories, and later demonstrated the proposed method on several numerical examples.…”

Solving fuzzy fractional differential equations using fuzzy Sumudu transform

“…In this paper, we propose a new solution of linear FFDEs involving Caputo fuzzy fractional derivative using FST. The FST is first proposed in [4] followed by [1]. Some other applications of FST can be seen in [23].…”

Fuzzy Sumudu transform for solving fuzzy partial differential equations

“…In order to construct the solution of FPDEs, first we adopted the definition of FST proposed in [1]. Then, two new results of FST for fuzzy partial derivative are introduced.…”

“…Recently, Ahmad and Abdul Rahman [1] proposed a fuzzy version of classical Sumudu transform called fuzzy Sumudu transform (FST). The authors successfully integrated the classical Sumudu transform into fuzzy setting.…”