STABILITY ANALYSIS OF NONLINEAR UNCERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO DERIVATIVE

Ziqiang Lu (), Yuanguo Zhu and Qinyun Lu ()
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Ziqiang Lu: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China
Yuanguo Zhu: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China
Qinyun Lu: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-10

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 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.

Keywords: Uncertainty Theory; Caputo Fractional Derivative; Uncertain Fractional Differential Equation; Stability in Measure (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500572

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