Existence and uniqueness results for fractional differential equations with uncertainty

Abstract

In this paper, we study the existence, uniqueness and approximate solutions of fuzzy fractional differential equations (FFDEs) under Caputo’s H-differentiability. To this end, the concept of Riemann-Liouville’s H-differentiability is introduced, and subsequently, the Caputo’s H-differentiability is proposed. Moreover, the related fuzzy Volterra integral forms of FFDEs are obtained which are applied to construct two converge consequences of fuzzy-valued functions as approximated solutions of FFDEs.