Generalized diffusion-wave equation with memory kernel
- We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.
Author details: | Trifce SandevORCiDGND, Zivorad TomovskiGND, Johan L. A. Dubbeldam, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8121/aaefa3 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/11/30 |
Publication year: | 2018 |
Release date: | 2021/04/21 |
Tag: | Mittag-Leffler function; anomalous diffusion; diffusion-wave equation |
Volume: | 52 |
Issue: | 1 |
Number of pages: | 22 |
Funding institution: | NWONetherlands Organization for Scientific Research (NWO) [040.11.629]; Foundation (DFG) [ME 1535/6-1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |