Abstract
The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.
Highlights
A fundamental problem in the process of modeling phenomena is the immense quantity and quality of information that has to be included, such that it is as representative as possible of the real system
Partial differential equations are mathematical equations that appear in a number of fields, such as physics, engineering, chemistry and biology
The objective of the present paper is to propose a stylish combination of the Adomian decomposition method [27,28] and fuzzy Sawi transformation that can solve nonlinear partial fuzzy differential equations
Summary
A fundamental problem in the process of modeling phenomena is the immense quantity and quality of information that has to be included, such that it is as representative as possible of the real system. The objective of the present paper is to propose a stylish combination of the Adomian decomposition method [27,28] and fuzzy Sawi transformation that can solve nonlinear partial fuzzy differential equations. When applying the fuzzy Sawi decomposition method to solve the nonlinear partial equation, we obtain a symmetry between the lower and upper representations of of the fuzzy solution. This paper is organized as follows: In Section 2, definitions on a fuzzy number, fuzzyvalued function and gH-Hukuhara differentiability are given. Let u and v be positive fuzzy numbers, w = u v defined by w(r) = [w(r), w(r)], where the following holds: w(r) = u(r)v(1) + u(1)v(r) − u(1)v(1).
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