STABILITY ANALYSIS OF NONLINEAR UNCERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO DERIVATIVE

Abstract

Uncertain fractional differential equation driven by Liu process plays a significant role in depicting the memory effects of uncertain dynamical systems. This paper mainly investigates the stability problems for the Caputo type of uncertain fractional differential equations with the order [Formula: see text]. The concept of stability in measure of solutions to uncertain fractional differential equation is proposed based on uncertainty theory. Several sufficient conditions for ensuring the stability of the solutions are derived, respectively, in which the systems are divided into two cases with order [Formula: see text] and [Formula: see text]. Some illustrative examples are performed to display the effectiveness of the proposed results.