A Yamazaki-type estimate to a space-time fractional diffusion equation

Authors

  • Maria Elismara de Sousa Lima Imecc - Universidade Estadual de Campinas
  • Edmundo Capelas de Oliveira Imecc - Universidade Estadual de Campinas
  • Arlúcio da Cruz Viana Universidade Federal de Sergipe

Keywords:

Yamazaki-type estimate, fractional diffusion equation, Mittag-Leffler family, decay in 𝐿𝑝 spaces.

Abstract

In this work, we develop the Yamazaki inequality and estimates of the Mittag-Leffler family associated with the space-time fractional diffusion equation in 𝐿𝑝-weak spaces. This result generalizes the inequality given by Yamazaki (2000) for the heat semigroup, which was generalized by Ferreira and VillamizarRoa (2006) for heat semigroup associated with the fractional Laplacian, and Caicedo et al (2021) for the Mittag-Leffler family associated with the time-fractional diffusion equation.

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Published

2022-09-28

How to Cite

LIMA, M. E. de S.; OLIVEIRA, E. C. de; VIANA, A. da C. A Yamazaki-type estimate to a space-time fractional diffusion equation. C.Q.D. - Revista Eletrônica Paulista de Matemática, Bauru, v. 22, n. 2, 2022. Disponível em: https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/312. Acesso em: 13 nov. 2024.

Issue

v.22, n.2 - Edição Brazilian Symposium on Fractional Calculus – Set/2022

Section

Artigos de Pesquisa

License

Copyright (c) 2022 C.Q.D. - Revista Eletrônica Paulista de Matemática

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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