Abstract—Differential equations has long become a very significant tool in modelling real-life problems and phenomena. Classical mathematics, via ordinary differential equations, however, failed to cope with the situations where uncertainty arise. It is well informed that in many cases, details and information of the physical phenomena are pervaded with uncertainty. Due to this, fuzzy differential equations (FDEs) become the best apparatus to model real-life phenomena. The main aim of this paper is to propose a novel procedure for solving FDEs through fuzzy Sumudu transform (FST). For this purpose, some basic concept and properties regarding to fuzzy concept and theories will be studied. The classical Sumudu transform is then extended into the fuzzy setting before solving FDEs. To make this happen, the FST will be interpreted under strongly generalized differentiability concept. Theorem on first degree derivative of FST will also be provided to describe the functionality of FST. Finally, a numerical example of solving FDEs using FST is given.

Index Terms—Fuzzy number, fuzzy sumudu transform, generalized differential, fuzzy differential equation.

The authors are with Institute of Engineering Mathematics, Universiti Malaysia Perlis, PauhPutra Main Campus, 02600 Arau, Perlis, Malaysia.

Cite: Muhammad Zaini Ahmad, Norazrizal Aswad bin Abdul Rahman, "Explicit Solution of Fuzzy Differential Equations by Mean of Fuzzy Sumudu Transform," International Journal of Applied Physics and Mathematics vol. 5, no. 2, pp. 86-93, 2015.