一类广义分数阶系统的Hyers-Ulam-Rassias稳定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1791-1804.

一类广义分数阶系统的Hyers-Ulam-Rassias稳定性

王春^1,*(),许天周²

¹ 长治学院数学系山西长治 046011
² 北京理工大学数学与统计学院北京 100081

收稿日期:2020-08-30 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 王春 E-mail:wangchun12001@163.com
基金资助:
山西省自然科学基金(201801D121024);山西省高等学校科技创新项目(2019L0903)

Hyers-Ulam-Rassias Stability on a Class of Generalized Fractional Systems

Chun Wang^1,*(),Tianzhou Xu²

¹ Department of Mathematics, Changzhi University, Shanxi Changzhi 046011
² School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081

Received:2020-08-30 Online:2021-12-26 Published:2021-12-02
Contact: Chun Wang E-mail:wangchun12001@163.com
Supported by:
the NSF of Shanxi Province(201801D121024);the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2019L0903)

摘要/Abstract

摘要：

该文应用广义Laplace变换方法研究了一类广义分数阶微分系统的Hyers-Ulam-Rassias稳定性，同时给出相关例子说明了理论结果的有效性.

关键词: 广义Laplace变换, 广义分数阶微分系统, Hyers-Ulam-Rassias稳定性

Abstract:

This paper investigates the stability in the sense of Hyers-Ulam-Rassias for a class of generalized fractional differential systems by the generalized Laplace transform method. Several examples are given to illustrate the theoretical results.

Key words: Generalized Laplace transform, Generalized fractional differential systems, Hyers-Ulam-Rassias stability

中图分类号:

O177.9

王春,许天周. 一类广义分数阶系统的Hyers-Ulam-Rassias稳定性[J]. 数学物理学报, 2021, 41(6): 1791-1804.

Chun Wang,Tianzhou Xu. Hyers-Ulam-Rassias Stability on a Class of Generalized Fractional Systems[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1791-1804.

参考文献 33

1	András S , Mészáros A R . Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl Math Comput, 2013, 219, 4853- 4864
2	Gejji V D , Babakhani A . Analysis of a system of fractional differential equations. J Math Anal Appl, 2004, 293, 511- 522 doi: 10.1016/j.jmaa.2004.01.013
3	Gordji M E , Cho Y , Ghaemi M , Alizadeh B . Stability of the second order partial differential equations. J Inequa Appl, 2011, 81, 1- 10
4	Hegyi B , Jung S M . On the stability of Laplace's equation. Appl Math Lett, 2013, 26, 549- 552 doi: 10.1016/j.aml.2012.12.014
5	Hyers D H . On the stability of the linear functional equation. Pro Natl Acad Sci USA, 1941, 27, 222- 224 doi: 10.1073/pnas.27.4.222
6	Jarad F , Abdeljawad T . Generalized fractional derivatives and Laplace transform. Discrete Contin Dyn Syst Ser S, 2020, 13, 709- 722
7	Jung S M . Hyers-Ulam stability of linear differential equations of first order. Appl Math Lett, 2004, 17, 1135- 1140 doi: 10.1016/j.aml.2003.11.004
8	Jung S M . Hyers-Ulam stability of linear differential equations of first order, Ⅲ. J Math Anal Appl, 2005, 311, 139- 146 doi: 10.1016/j.jmaa.2005.02.025
9	Jung S M . Hyers-Ulam stability of linear differential equations of first order, Ⅱ. Appl Math Lett, 2006, 19, 854- 858 doi: 10.1016/j.aml.2005.11.004
10	Jung S M . Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients. J Math Anal Appl, 2006, 320, 549- 561 doi: 10.1016/j.jmaa.2005.07.032
11	Kilbas A A , Srivastava H M , Trujillo J J . Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006
12	Li K , Peng J . Laplace transform and fractional differential equations. Appl Math Lett, 2011, 24, 2019- 2023 doi: 10.1016/j.aml.2011.05.035
13	Lungu N , Popa D . Hyers-Ulam stability of a first order partial differential equation. J Math Anal Appl, 2012, 385, 86- 91 doi: 10.1016/j.jmaa.2011.06.025
14	Obloza M . Hyers stability of the linear differential equation. Rocznik Nauk-Dydakt Prace Mat, 1993, 13, 259- 270
15	Obloza M . Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Nauk-Dydakt Prace Mat, 1997, 14, 141- 146
16	Podlubny I . Fractional Differential Equations. San Diego: Academic Press, 1999
17	Popa D , Raşa I . On the Hyers-Ulam stability of the linear differential equation. J Math Anal Appl, 2011, 381, 530- 537 doi: 10.1016/j.jmaa.2011.02.051
18	Rassias Th M . On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc, 1978, 72, 297- 300 doi: 10.1090/S0002-9939-1978-0507327-1
19	Rezaei H , Jung S M , Rassias T M . Laplace transform and Hyers-Ulam stability of linear differential equations. J Math Anal Appl, 2013, 403, 244- 251 doi: 10.1016/j.jmaa.2013.02.034
20	Shen Y , Chen W . Laplace transform method for the Ulam stability of linear fractional differential equations with constant coefficients. Mediterr J Math, 2017, 14, 1- 17 doi: 10.1007/s00009-016-0833-2
21	Sun H G , Zhang Y , Baleanu D , et al. A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlinear Sci Numer Simul, 2018, 64, 213- 231 doi: 10.1016/j.cnsns.2018.04.019
22	Ulam S M . Problems in Modern Mathematics. New York: Wiley, 1960
23	Wang J , Zhou Y . Mittag-Leffler-Ulam stabilities of fractional evolution equations. Appl Math Lett, 2012, 25, 723- 728 doi: 10.1016/j.aml.2011.10.009
24	Wang J , Li X . A uniform method to Ulam-Hyers stability for some linear fractional equations. Mediterr J Math, 2016, 13, 625- 635 doi: 10.1007/s00009-015-0523-5
25	Wang C, Xu T Z. Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions. J Funct Spaces, 2014, 2014: Article ID: 398673
26	Wang C , Xu T Z . Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives. Appl Math, 2015, 60, 383- 393 doi: 10.1007/s10492-015-0102-x
27	Wang C , Xu T Z . Hyers-Ulam stability of differential operators on reproducing kernel function spaces. Complex Anal Oper Theory, 2016, 10, 795- 813 doi: 10.1007/s11785-015-0486-3
28	Wang C , Xu T Z . Hyers-Ulam stability of a class of fractional linear differential equations. Kodai Math J, 2015, 38, 510- 520
29	Wang C , Xu T Z . Stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville fractional derivative. Discrete Contin Dyn Syst Ser S, 2017, 10, 505- 521
30	Wang C. Hyers-Ulam-Rassias stability of the generalized fractional systems and the ρ-Laplace transform method. Mediterr J Math, 2021, 18(4): Article number: 129
31	Xu T Z , Wang C , Rassias Th M . On the stability of multi-additive mappings in non-Archimedean normed spaces. J Comput Anal Appl, 2015, 18, 1102- 1110
32	Xu T Z . On the stability of multi-Jensen mappings in β-normed spaces. Appl Math Lett, 2012, 25, 1866- 1870 doi: 10.1016/j.aml.2012.02.049
33	王春. 一类分数阶系统的稳定性和Laplace变换. 数学物理学报, 2019, 39A (1): 49- 58 doi: 10.3969/j.issn.1003-3998.2019.01.005
	Wang C . Stability of some fractional systems and Laplace transform. Acta Math Sci, 2019, 39A (1): 49- 58 doi: 10.3969/j.issn.1003-3998.2019.01.005

[1]	王春,许天周. 2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性[J]. 数学物理学报, 2020, 40(2): 352-368.
[2]	王春. 一类分数阶系统的稳定性和Laplace变换[J]. 数学物理学报, 2019, 39(1): 49-58.
[3]	王春, 许天周. 拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性[J]. 数学物理学报, 2017, 37(5): 846-859.