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arXiv · 2111.01197

Special Solutions to the Space Fractional Diffusion Problem

Tokinaga Namba·Piotr Rybka·Shoichi Sato
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Abstract

We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the Dirichlet and Neumann problems in terms of convolution of $\mathscr{E}$ with data. We also study integrability of derivative of solutions given in this way. We present conditions sufficient for uniqueness. Finally, we show the infinite speed of signal propagation.

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Tokinaga Namba, Piotr Rybka, Shoichi Sato. 2021-11-01. Special Solutions to the Space Fractional Diffusion Problem. https://arxiv.org/abs/2111.01197

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