Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses

Abstract

A partir de la expresión de la solución exacta de un problema de frontera periódico para una ecuación diferencial con impulsos de primer orden obtenemos la extensión para el caso difuso probando la existencia y unicidad de solución.

Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order linear fuzzy differential equation with impulses subject to boundary value conditions. We obtain the explicit solution by calculating the solutions on each level set and justify that the parametric functions obtained define a proper fuzzy function. Our results prove that the solution of the fuzzy differential equation of interest is determined, under the appropriate conditions, by the same Green s function obtained for the real case. Thus, the results proved extend some theorems given for ordinary differential equations.