Existence, Uniqueness, and <i>E</i>_q–Ulam-Type Stability of Fuzzy Fractional Differential Equation

Abstract

This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.

Keywords

• fuzzy fractional differential equations
• Caputo derivative
• fractional hyperbolic function
• strongly generalized Hukuhara differentiability
• Ulam-type stability