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Questions regarding derivatives and integrals of non-integer order.

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How to check that $f(t,x)\ge 0$ for any $x\ge 0$?

Suppose $f(t,x)$ satisfices $\partial_t f=\Lambda^{-\alpha}f\partial_xf$, for $0<\alpha<1$ and where $\Lambda=(-\partial_{xx})^{1/2}$, $f_0(x)=f(0,x)$ is odd, and $f_0(x)\ge 0$, $\forall x\ge 0$. We c …
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