Fuzzy Sumudu Decomposition Method for Fuzzy Delay Differential Equations with Strongly Generalized Differentiability

Abstract

Fuzzy delay differential equation has always been a tremendous way to model real-life problems. It has been developed throughout the last decade. Many types of fuzzy derivatives have been considered, including the recently introduced concept of strongly generalized differentiability. However, considering this interpretation, very few methods have been introduced, obstructing the potential of fuzzy delay differential equations to be developed further. This paper aims to provide solution for fuzzy nonlinear delay differential equations and the derivatives considered in this paper is interpreted using the concept of strongly generalized differentiability. Under this method, the calculations will lead to two cases i.e. two solutions, and one of the solutions is decreasing in the diameter. To fulfil this, a method resulting from the elegant combination of fuzzy Sumudu transform and Adomian decomposition method is used, it is termed as fuzzy Sumudu decomposition method. A detailed procedure for solving fuzzy nonlinear delay differential equations with the mentioned type of derivatives is constructed in detail. A numerical example is provided afterwards to demonstrate the applicability of the method. It is shown that the solution is not unique, and this is in accord with the concept of strongly generalized differentiability. The two solutions can later be chosen by researcher with regards to the characteristic of the problems. Finally, conclusion is drawn.