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 SandevORCiD, Zivorad TomovskiGND, Johan L. A. Dubbeldam, Aleksei V. ChechkinORCiDGND |
|---|---|
| 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 |
