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

页码：1663 / 1677

页数：15

共 50 条

[21] On the computation of the multidimensional Mittag-Leffler function
Ortigueira, Manuel D.
Lopes, Antonio M.
Tenreiro Machado, J. A.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 53 : 278 - 287
[22] Mittag-Leffler functions in superstatistics
dos Santos, Maike A. F.
CHAOS SOLITONS & FRACTALS, 2020, 131
[23] A FAMILY OF MEROMORPHIC FUNCTIONS INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION
Yan, Cai-Mei
Liu, Jin-Lin
JOURNAL OF MATHEMATICAL INEQUALITIES, 2018, 12 (04): : 943 - 951
[24] STARLIKENESS AND CONVEXITY OF INTEGRAL OPERATORS INVOLVING MITTAG-LEFFLER FUNCTIONS
Frasin, B. A.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2024, 14 (03): : 913 - 920
[25] A comprehensive class of starlike functions involving Mittag-Leffler function
Karthikeyan, Kadhavoor R.
Mohankumar, Dharmaraj
Breaz, Daniel
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, 2025, 33 (01):
[26] On van der Corput-type lemmas for Bessel and Airy transforms and applications
Xiang, Shuhuang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 351 : 179 - 185
[27] Mapping properties of Janowski-type harmonic functions involving Mittag-Leffler function
Gangadharan, Murugusundaramoorthy
Kaliyappan, Vijaya
Ahmad, Hijaz
Mahmoud, K. H.
Khalil, E. M.
AIMS MATHEMATICS, 2021, 6 (12): : 13235 - 13246
[28] Fractional integrals and derivatives of Mittag-Leffler type functions
Kilbas, AA
Saigo, M
DOKLADY AKADEMII NAUK BELARUSI, 1995, 39 (04): : 22 - 26
[29] On differentiation with respect to parameters of the functions of the Mittag-Leffler type
Rogosin, Sergei V.
Giraldi, Filippo
Mainardi, Francesco
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2024,
[30] Approximation by meromorphic functions with Mittag-Leffler type constraints
Gauthier, PM
Pouryayevali, MR
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2001, 44 (04): : 420 - 428

← 1 2 3 4 5 →