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- Copyright
- Copyright © 2018 IOP Publishing Ltd
- ISSN
- 1751-8113
- eISSN
- 1751-8121
- DOI
- 10.1088/1751-8121/aaefa3
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Journal of Physics A: Mathematical and Theoretical – IOP Publishing
Published: Jan 4, 2019