On the solutions to first order linear fuzzy differential equations
The authors study the solvability of different types of first order linear fuzzy differential equations, from the point of view of generalized differentiability and give optimal sufficient (also necessary) conditions for the existence of solution to the initial value problem related, respectively, to the equations \[ y'(t)=a(t)y(t)+b(t), \,\, y'(t)+(-a(t))y(t)=b(t)\,\, \text{and}\,\,y'(t)+(-b(t))=a(t)y(t) \] obtaining also the explicit expressions of the solutions. The authors prove that the same expressions can be solutions to different problems, depending on the existence of the appropriate type of Hukuhara differences. Some examples illustrate these results.
first-order fuzzy differential equations
scientific article; zbMATH DE number 6806597
scientific article