ON A NON-LOCAL PROBLEM FOR A MULTI-TERM FRACTIONAL DIFFUSION-WAVE EQUATION

被引：28
|
作者：
Ruzhansky, Michael [1 ,2 ]
Tokmagambetov, Niyaz [1 ,3 ,4 ]
Torebek, Berikbol T. [1 ,3 ,4 ]
机构：
[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Krijgslaan 281,Bldg S8, B-9000 Ghent, Belgium
[2] Queen Mary Univ London, Sch Math Sci, London, England
[3] Al Farabi Kazakh Natl Univ, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan
[4] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
time-fractional diffusion-wave equation; Caputo derivative; nonlocal-initial problem; multivariate Mittag-Leffler function; self-adjoint operator; BOUNDARY-VALUE-PROBLEMS; WEAK SOLUTIONS; OPERATORS; PRINCIPLE;
D O I：
10.1515/fca-2020-0016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：324 / 355
页数：32
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