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.
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