Positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability

Abstract

The purpose of this paper is to study solutions to a class of first-order fully fuzzy linear differential equations from the point of view of generalized differentiability. The article begins with considering and analyzing the positive or negative fuzzy-valued functions defined on a real interval. Some of the topics which are needed for the results of this study, such as continuity and differentiability of the product of fuzzy-valued functions and also the derivative of fuzzy-valued exponential functions have been explained, in details. Then, we obtain the solution functions and necessary and sufficient conditions of their existence based on the solutions found from systems of ordinary differential equations. Finally, some applications are presented and some examples are brought to show the desirable behavior of the obtained solutions.