## Abstract

We introduce a weighted Lp-theory (p > 1) for the time-fractional diffusion-wave equation of the type ∂_{t}^{α}u(t, x) = a^{ij}(t, x)u_{x}i_{x}j (t, x) + f(t, x), t > 0, x ∈ Ω, where α ∈ (0, 2), ∂_{t}^{α} denotes the Caputo fractional derivative of order α, and Ω is a C^{1} domain in R^{d}. We prove existence and uniqueness results in Sobolev spaces with weights which allow derivatives of solutions to blow up near the boundary. The order of derivatives of solutions can be any real number, and in particular it can be fractional or negative.

Original language | English |
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Pages (from-to) | 3415-3445 |

Number of pages | 31 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Volume | 41 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2021 Jul |

## Keywords

- Caputo fractional derivative
- Domains domains
- Sobolev space with weights
- Time-fractional equation
- Variable coefficients

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

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