The authors prove Ulam-Hyers and Ulam-Hyers-Rassias stability for mild solutions of a Hilfer fractional abstract Cauchy problem on [0,T] and [0,∞) using the Banach fixed point theorem.
On the uniqueness of mild solutions to the time-fractional Navier-Stokes equations in $L^{N} \left( \mathbb{R} ^{N}\right) ^{N} $
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abstract
In this paper, we present the result of maximum regularity of the mild solution of the fractional Cauchy problem. As our main result, we investigate the uniqueness of mild solutions for time-fractional Navier-Stokes equations in class $C\left([0,\infty);L^{N}\left( \mathbb{R}^{N}\right)^{N}\right)$ by means of the estimates $L^{p}-L^{q}$ of Giga-Shor inequality and the Gronwall inequality.
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math.CA 1years
2019 1verdicts
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Ulam-Hyers stabilities of mild solutions of the fractional nonlinear abstract Cauchy problem
The authors prove Ulam-Hyers and Ulam-Hyers-Rassias stability for mild solutions of a Hilfer fractional abstract Cauchy problem on [0,T] and [0,∞) using the Banach fixed point theorem.