Solutions of fuzzy differential equations based on generalized differentiability

Abstract

The main goal of this paper is to show that the concept of generalized differentiability introduced by the authors in [2] allows to obtain new solutions to the fuzzy differential equations. A very general existence and uniqueness result of two solutions for the fuzzy differential equations with modified argument and based on generalized differentiability is obtained together with a characterization of these solutions by ODEs. Real-world applications consisting in applications to fuzzy pantograph equation that models the cell growth and to fuzzy logistic equation that models the population dynamics under uncertainty are presented. In particular, as collateral consequences we correct some results on generalized differentiability recently obtained by Y. Chalco-Cano and H. Román-Flores in [7]and propagated in a characterization result obtained by J.J. Nieto, A. Khastan and K. Ivaz in [21].