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In this article, we consider the Cauchy problem for the following time-space fractional pseudo-parabolic equations where . An estimating for solution operator of time-space fractional pseudo-parabolic equations is obtained. The critical exponents of this problem are determined when Moreover, we also obtain global existence of the mild solution when small enough. [ABSTRACT FROM AUTHOR]

This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when α < γ and α ≥ γ , respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents. [ABSTRACT FROM AUTHOR]

In this paper, we consider a time fractional diffusion system with a nonlinear memory term in a bounded domain. We mainly prove some blow-up and global existence results for this problem. Moreover, we also give the decay estimates of the global solutions. Our proof relies on the eigenfunction method combined with the asymptotic behavior of the solution of a fractional differential inequality system, the estimates of the solution operators and the asymptotic behavior of the Mittag–Leffler function. In particular, we give the critical exponents of this problem in different cases. Our results show that, in some cases, whether one of the initial values is identically equal to zero has a great influence on blow-up and global existence of the solutions for this problem, which is a remarkable property of time fractional diffusion systems because the classical diffusion systems can not admit this property. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we prove sharp blow-up and global existence results for a time fractional subdiffusion equation with nonlinear memory in a bounded domain. The critical exponents of this problem are determined when α < γ and α ≥ γ , respectively. [ABSTRACT FROM AUTHOR]

In this paper, we determine the Fujita critical exponent of the following time fractional subdiffusion equation with nonlinear memory 0CDtαu−△u=0It1−γ|u|p−1u,x∈RN,t>0,u(0,x)=u0(x),x∈RN,where 0 < α < 1, 0 ≤ γ < 1, γ ≤ α, p > 1, u0∈C0RN, 0It1−γ denotes left Riemann‐Liouville fractional integral of order 1 − γ. Let β = 1 − γ. We prove that, if 1 p∗ and ‖u0‖LqcRN is sufficiently small, where qc=Nα(p−1)2(α+β), then u exists globally. [ABSTRACT FROM AUTHOR]

We prove sharp blow-up and global existence results for the Cauchy problem of a time fractional diffusion system when initial values u 0 ⁄ ≡ 0 and v 0 ⁄ ≡ 0. The critical exponent of this problem is determined. [ABSTRACT FROM AUTHOR]