Solution of linear ordinary differential equations in a fuzzy environment by method of variation of parameters (Journal of Pure and Applied Sciences (Science Forum), 2026)
This work considers linear fuzzy initial value problems (LFIVPs) defined under gH-differentiability with the aim of establishing a method and, subsequently, a fuzzy-valued function, 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.