Exp-type Ulam-Hyers stability of fractional differential equations with positive constant coefficient

被引：0

作者：

Zhuoyan Gao

Xiulan Yu

JinRong Wang

机构：

[1] Shanxi University of Finance and Economics,College of Applied Mathematics

[2] Guizhou University,Department of Mathematics

来源：

Advances in Difference Equations | / 2015卷

关键词：

26A33; 34D10; 45N05; exp-type Ulam-Hyers stability; fractional differential equations; asymptotic behavior;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we apply asymptotic behavior on Mittag-Leffler functions Eα(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{E}_{\alpha}(z)$\end{document} and Eα,α(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{E}_{\alpha,\alpha}(z)$\end{document} for z>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$z>0$\end{document} to discuss exp-type Ulam-Hyers stability of Dtαcx(t)=λx(t)+f(t,x(t))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}^{\mathrm{c}} D_{t}^{\alpha}x(t)=\lambda x(t)+f(t,x(t))$\end{document} for the case λ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda>0$\end{document} on a finite time interval [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[0,1]$\end{document} and an unbounded interval (1,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(1,\infty)$\end{document}.

引用

共 25 条

[1]

Brzdȩk J(2012)Ulam’s type stability Abstr. Appl. Anal. 2012 125-133

[2]

Brillouët-Belluot N(2009)Ulam stability of ordinary differential equations Stud. Univ. Babeş-Bolyai, Math. 54 530-537

[3]

Ciepliński K(2011)On the Hyers-Ulam stability of the linear differential equation J. Math. Anal. Appl. 381 549-552

[4]

Xu B(2013)On the stability of Laplace’s equation Appl. Math. Lett. 26 449-459

[5]

Rus IA(2014)-Ulam type stability of fractional order ordinary differential equations J. Appl. Math. Comput. 45 1855-1872

[6]

Popa D(2013)Presentation of solutions of impulsive fractional Langevin equations and existence results Eur. Phys. J. Spec. Top. 222 1075-1081

[7]

Raşa I(2007)A generalized Gronwall inequality and its application to a fractional differential equation J. Math. Anal. Appl. 328 222-224

[8]

Hegyi B(1941)On the stability of the linear functional equation Proc. Natl. Acad. Sci. USA 27 491-518

[9]

Jung S-M(2002)Computation of the Mittag-Leffler function Fract. Calc. Appl. Anal. 5 157-168

[10]

Wang J(2014) and its derivative Appl. Math. Comput. 226 undefined-undefined

← 1 2 3 →