On a non–local problem for a multi–term fractional diffusion-wave equation-Reference-Cited by-同舟云学术

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

Published:2020-04-01 Issue:2 Volume:23 Page:324-355
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Ruzhansky Michael¹²,Tokmagambetov Niyaz¹³⁴,Torebek Berikbol T.¹³⁴

Affiliation:

1. Department of Mathematics: Analysis, Logic and Discrete Mathematics , Ghent University , Krijgslaan 281 Building S8 B 9000 , Ghent , Belgium

2. School of Mathematical Sciences , Queen Mary University of London , London , United Kingdom

3. Al–Farabi Kazakh National University , 71 Al–Farabi ave ., Almaty , 050040 , Kazakhstan

4. Institute of Mathematics and Mathematical Modeling , 125 Pushkin str ., Almaty , 050010 , Kazakhstan

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0016/pdf

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