Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability

We study the existence of solutions to a class of first-order linear fuzzy differential equations subject to periodic boundary conditions from the point of view of generalized differentiability. The objective of this paper is to show that fuzzy differential equations under generalized differentiability can be used in the study of periodic phenomena, by considering a combination of two types of derivatives with a switching point. We provide sufficient conditions which guarantee that the piecewise-defined solutions match adequately and illustrate, through some examples, the process of construction and calculation of solutions.