STABILITY ANALYSIS OF NONLINEAR UNCERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO DERIVATIVE

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 0 < p <= 1. 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 1/2 < p <= 1 and 0 < p <= 1/2. Some illustrative examples are performed to display the effectiveness of the proposed results.

Automated summary

This paper investigates the stability problems for Caputo type of uncertain fractional differential equations with the order 0 < p <= 1 driven by Liu process, proposing a concept of stability in measure of solutions and deriving several sufficient conditions for stability in two different order cases. Illustrative examples are performed to demonstrate the effectiveness of the proposed results.