Special Solutions to the Space Fractional Diffusion Problem
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2021
- DOI:
- 10.48550/arXiv.2111.01197
- arXiv:
- arXiv:2111.01197
- Bibcode:
- 2021arXiv211101197N
- Keywords:
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- Mathematics - Analysis of PDEs;
- Primary: 35R11;
- Secondary: 35A08
- E-Print:
- 17 pages, no figures