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On the stability and global attractivity of solutions of fractional partial differential equations with uncertainty

Authors: 

Nguyen Thi Kim Son, Ha Thi Thanh Tam

Source title: 
Journal of Intelligent & Fuzzy Systems, 35(3): 3797-3806, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

In this paper, we study fractional partial differential equations (FPDEs) under Caputo gH-differentiability with uncertainty in type of fuzziness. Using Banach fixed point theorem, we show that the equilibrium point of the problem is stable. The stability is understood in the sense of Lyapunov stability. Moreover, by constructing a basic space of integral solutions, we prove global existence of fuzzy decay solutions of the problem. Some examples are also given to illustrate our main results.