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On a non–local problem for a multi–term fractional diffusion-wave equation

  • Michael Ruzhansky EMAIL logo , Niyaz Tokmagambetov and Berikbol T. Torebek


This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions. Several examples of the settings where our nonlocal problems are applicable are given. The results for the discrete spectrum are also applied to treat the case of general homogeneous hypoelliptic left-invariant differential operators on general graded Lie groups, by using the representation theory of the group. For all these problems, we show the existence, uniqueness, and the explicit representation formulae for the solutions.


The authors were supported in parts by the FWO Odysseus Project 1 Grant G.0H94.18N: Analysis and Partial Differential Equations. The first author was supported in parts by the EPSRC Grant EP/R003025/1 and by the Leverhulme Grant RPG-2017-151. The second author was supported by the Ministry of Education and Science of the Republic of Kazakhstan Grant AP05130994. The third author was supported by Ministry of Education and Science of the Republic of Kazakhstan Grant AP05131756. No new data were collected or generated during the course of research.


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Received: 2018-12-04
Published Online: 2020-05-09
Published in Print: 2020-04-28

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