MULTIDIMENSIONAL VAN DER CORPUT-TYPE ESTIMATES INVOLVING MITTAG-LEFFLER FUNCTIONS

被引：5
|
作者：
Ruzhansky, Michael [1 ,2 ]
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 / 06期
基金：
英国工程与自然科学研究理事会;
关键词：
van der Corput-type estimates; Mittag-Leffler function; time-fractional Schrodinger equation; time-fractional Klein-Gordon equation; BESSEL;
D O I：
10.1515/fca-2020-0082
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E-alpha,E-beta(i lambda phi(x)), x is an element of R-N and E-alpha,E-beta(i(alpha)lambda phi(x)), x is an element of R-N for the various range of alpha and beta. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrodinger equations are considered.
引用
收藏
页码：1663 / 1677
页数：15
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