Generalized diffusion-wave equation with memory kernel

Trifce Sandev, Zhivorad Tomovski, Johan L.A. Dubbeldam, Aleksei Chechkin

Research output: Contribution to journalArticleScientificpeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Article number015201
Pages (from-to)1-23
Number of pages23
JournalJournal of Physics A: Mathematical and Theoretical
Publication statusPublished - 2019


  • anomalous diffusion
  • diffusion-wave equation
  • Mittag-Leffler function

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