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For the following semilinear equation with Hilfer- Hadamard fractional derivative begin{equation*} mathcal{D}^{alpha_1,beta}_{a^+} u-Deltamathcal{D}^{alpha_2,beta}_{a^+} u-Delta u =vert uvert^p, qquad t>a>0, qquad xinOmega, end{equation*} where $Omegasubset mathbb{R}^N$ $(Ngeqslant 1)$, $p>1$, $0<alpha _{2}<alpha _{1}<1$ and $0<beta <1$. $mathcal{D}^{alpha_i,beta}_{a^+}$ $(i=1,2)$ is the Hilfer- Hadamard fractional derivative of order $alpha_i$ and of type $beta$, we establish the necessary conditions for the existence of global solutions.
We study fractional parabolic equations with indefinite nonlinearities $$ frac{partial u} {partial t}(x,t) +(-Delta)^s u(x,t)= x_1 u^p(x, t),,, (x, t) in mathbb{R}^n times mathbb{R}, $$ where $0<s<1$ and $1<p<infty$. We first prove that all positive
We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, anomalous relaxati
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.
We study existence and non-existence of global solutions to the semilinear heat equation with a drift term and a power-like source term, on Cartan-Hadamard manifolds. Under suitable assumptions on Ricci and sectional curvatures, we show that global s
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fra