ON AN EQUATION BEING A FRACTIONAL DIFFERENTIAL EQUATION WITH RESPECT TO TIME AND A PSEUDO-DIFFERENTIAL EQUATION WITH RESPECT TO SPACE RELATED TO LEVY-TYPE PROCESSES

被引：2

作者：

Hu, Ke ^{[1
]}

Jacob, Niels ^{[1
]}

Yuan, Chenggui ^{[1
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2012年 / 15卷 / 01期

关键词：

fractional differential equation; Mittag-Leffler functions; pseudo-differential operator; Laplace transform; Fourier transform; DIFFUSION;

D O I：

10.2478/s13540-012-0009-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of fractional differential equations are investigated. Using estimates for Mittag-Leffler function and a fixed point theorem, we establish the existence and uniqueness of mild solutions of the equations.

引用

页码：128 / 140

页数：13

共 50 条

[1] On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes
Ke Hu
Niels Jacob
Chenggui Yuan
Fractional Calculus and Applied Analysis, 2012, 15 : 128 - 140
[2] Convexity with respect to a differential equation
Ferreira, OP
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 315 (02) : 626 - 641
[3] On a nonlinear stochastic pseudo-differential equation driven by fractional noise
Liu, Junfeng
Yan, Litan
STOCHASTICS AND DYNAMICS, 2018, 18 (01)
[4] SOLVING A NONLINEAR PSEUDO-DIFFERENTIAL EQUATION OF BURGERS TYPE
Jacob, Niels
Potrykus, Alexander
Wu, Jiang-Lun
STOCHASTICS AND DYNAMICS, 2008, 8 (04) : 613 - 624
[5] On a Pseudo-Differential Equation¶for Stokes Waves
J. F. Toland
Archive for Rational Mechanics and Analysis, 2002, 162 : 179 - 189
[6] On a pseudo-differential equation for Stokes waves
Toland, JF
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 162 (02) : 179 - 189
[7] When is a pseudo-differential equation solvable?
Lerner, N
ANNALES DE L INSTITUT FOURIER, 2000, 50 (02) : 443 - +
[8] A differential equation of the second order with respect to time in a domain with moving boundary
Sil'chenko, YT
DIFFERENTIAL EQUATIONS, 2001, 37 (02) : 309 - 311
[9] A Differential Equation of the Second Order with Respect to Time in a Domain with Moving Boundary
Yu. T. Sil'chenko
Differential Equations, 2001, 37 : 309 - 311
[10] On a stochastic fractional partial differential equation driven by a Levy space-time white noise
Shi, Kehua
Wang, Yongjin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 364 (01) : 119 - 129

← 1 2 3 4 5 →