The Mittag-Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation

被引：4

作者：

Dorrego, Gustavo A. ^{[1
]}

机构：

[1] Northeast Natl Univ, Fac Exacts Sci, Dept Math, Corrientes, Argentina

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2016年 / 27卷 / 05期

关键词：

Mittag-Leffler-type function; Riemann-Liouville fractional derivative; Fractional differential equation; Hilfer fractional derivative; Caputo fractional derivative; integrals transforms; Fox's H-function; ultra-hyperbolic operator; 33E20; 26A33; 33E12; 35R11; FUNDAMENTAL-SOLUTIONS;

D O I：

10.1080/10652469.2016.1144185

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in the Hilfer sense. The analytical solution is obtained in terms of the Fox's H-function, for which the inverse Fourier transform of a Mittag-Leffler-type function that contains in its argument a positive-definite quadratic form is calculated.

引用

页码：392 / 404

页数：13

共 50 条

[21] An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law
Hosseini, Kamyar
Ilie, Mousa
Mirzazadeh, Mohammad
Baleanu, Dumitru
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (08) : 6247 - 6258
[22] Cauchy and Signaling Problems for the Time-Fractional Diffusion-Wave Equation
Luchko, Yuri
Mainardi, Francesco
[J]. JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2014, 136 (05):
[23] Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates
Povstenko, Y. Z.
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2011,
[24] Stochastic processes related to time-fractional diffusion-wave equation
Gorenflo, Rudolf
[J]. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 2015, 6 (02):
[25] Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates
Y.Z. Povstenko
[J]. Advances in Difference Equations, 2011
[26] Fractional wave equation with a frictional memory kernel of Mittag-Leffler type
Tomovski, Zivorad
Sandev, Trifce
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (20) : 10022 - 10031
[27] Matrix Mittag-Leffler function in fractional systems and its computation
Matychyn, I.
Onyshchenko, V.
[J]. BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES, 2018, 66 (04) : 495 - 500
[28] Variable-order time-fractional diffusion equation with Mittag-Leffler kernel: regularity analysis and uniqueness of determining variable order
Guo, Xu
Zheng, Xiangcheng
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (02):
[29] Variable-order time-fractional diffusion equation with Mittag-Leffler kernel: regularity analysis and uniqueness of determining variable order
Xu Guo
Xiangcheng Zheng
[J]. Zeitschrift für angewandte Mathematik und Physik, 2023, 74
[30] Approximate-analytical iterative approach to time-fractional Bloch equation with Mittag-Leffler type kernel
Akshey
Singh, Twinkle R.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (08) : 7028 - 7045

← 1 2 3 4 5 →