Solution of linear ordinary differential equations in a fuzzy environment by method of variation of parameters

Abstract

This work considers linear fuzzy initial value problems (LFIVPs) defined under gH-differ
entiability with the aim of establishing a method and, subsequently, a fuzzy-valued func
tion, which is a solution to the LFIVPs. The conditions for a fuzzy function to be Hukuhara 
(H)-differentiable and gH-differentiability are defined. It is, however, established that 
the gH-differentiability concept to fuzzy-valued functions is more generalized than 
H-differentiable. Characterization and stacking theorems are also used to translate LFIVPs 
to a system of specialized ODEs. The method of variation of parameters is also extended 
to LFIVPs. Examples are constructed to test the applicability of the methods and graphical 
presentation of the behavior of solutions of the constructed examples is carried out with 
the aid of MATLAB version 8.5. We recommend that further studies should be carried out 
on second and higher order LFIVPs.