一类分数阶系统的稳定性和Laplace变换
|
摘要
该文研究了一类分数阶微分系统的Hyers-Ulam-Rassias稳定性.主要应用Laplace变换方法证明了这类分数阶系统是Hyers-Ulam-Rassias稳定的.通过具体的例子说明了所得理论结果的有效性.
This paper investigates the Hyers-Ulam-Rassias stability of a kind of fractional differential systems, and proves that this kind of fractional differential systems are Hyers-UlamRassias stable by the Laplace transform method. Two examples are given to illustrate the theoretical results.
This paper investigates the Hyers-Ulam-Rassias stability of a kind of fractional differential systems, and proves that this kind of fractional differential systems are Hyers-UlamRassias stable by the Laplace transform method. Two examples are given to illustrate the theoretical results.
引文
[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
[3] Gordji M E, Cho Y, Ghaemi M, Alizadeh B. Stability of the second order partial differential equations. J Inequal 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
[5] Jung S M. Hyers-Ulam stability of linear differential equations of first order. Appl Math Lett, 2004, 17:1135-1140
[6] Jung S M. Hyers-Ulam stability of linear differential equations of first order,Ⅲ. J Math Anal Appl, 2005,311:139-146
[7] Jung S M. Hyers-Ulam stability of linear differential equations of first order,Ⅱ. Appl Math Lett, 2006, 19:854-858
[8] 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
[9] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations.Amsterdam:Elsevier, 2006
[10] Li K, Peng J. Laplace transform and fractional differential equations. Appl Math Lett, 2011, 24:2019-2023
[11] Lungu N,Popa D. Hyers-Ulam stability of a first order partial differential equation. J Math Anal Appl,2012, 385:86-91
[12] Obloza M. Hyers stability of the linear differential equation. Rocznik Nauk-Dydakt Prace Mat, 1993, 13:259-270
[13] Obloza M. Connections between Hyers and Lyapunov stability of the ordinary differential equations.Rocznik Nauk-Dydakt Prace Mat, 1997, 14:141-146
[14] Podlubny I. Fractional Differential Equations. San Diego:Academic Press, 1999
[15] Popa D, Rasa I. On the Hyers-Ulam stability of the linear differential equation. J Math Anal Appl, 2011,381:530-537
[16] 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
[17] 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
[18] Wang J, Zhou Y. Mittag-Leffler-Ulam stabilities of fractional evolution equations. Appl Math Lett, 2012,25:723-728
[19] Wang J, Li X. A uniform method to Ulam-Hyers stability for some linear fractional equations. Mediterr J Math, 2016, 13:625-635
[20] 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
[21] Wang C, Xu T Z. Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives. Appl Math, 2015, 60:383-393
[22] Wang C, Xu T Z. Hyers-Ulam stability of differential operators on reproducing kernel function spaces.Complex Anal Oper Theory, 2016, 10:795-813
[23] Wang C, Xu T Z. Hyers-Ulam stability of a class of fractional linear differential equations. Kodai Math J,2015, 38:510-520
[24] Wang C, Xu T Z. Stability of the nonlinear fractional differential equations with the right-sided RiemannLiouville fractional derivative. Discrete Contin Dyn Syst Ser S, 2017, 10:505-521
[25] Xu T Z, Wang C, Rassias T M. On the stability of multi-additive mappings in non-Archimedean normed spaces. J Comput Anal Appl, 2015, 18:1102-1110
[26] Xu T Z. On the stability of multi-Jensen mappings inβ-normed spaces. Appl Math Lett, 2012, 25:1866-1870
[27]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.数学物理学报,2017, 37A(5):846-859Wang C, Xu T Z. Solution and Hyers-Ulam-Rassias stability of a mixed type quadratic-additive functional equation with a parameter in quasi-Banach spaces. Acta Math Sci, 2017, 37A(5):846-859
[2] Gejji V D, Babakhani A. Analysis of a system of fractional differential equations. J Math Anal Appl, 2004,293:511-522
[3] Gordji M E, Cho Y, Ghaemi M, Alizadeh B. Stability of the second order partial differential equations. J Inequal 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
[5] Jung S M. Hyers-Ulam stability of linear differential equations of first order. Appl Math Lett, 2004, 17:1135-1140
[6] Jung S M. Hyers-Ulam stability of linear differential equations of first order,Ⅲ. J Math Anal Appl, 2005,311:139-146
[7] Jung S M. Hyers-Ulam stability of linear differential equations of first order,Ⅱ. Appl Math Lett, 2006, 19:854-858
[8] 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
[9] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations.Amsterdam:Elsevier, 2006
[10] Li K, Peng J. Laplace transform and fractional differential equations. Appl Math Lett, 2011, 24:2019-2023
[11] Lungu N,Popa D. Hyers-Ulam stability of a first order partial differential equation. J Math Anal Appl,2012, 385:86-91
[12] Obloza M. Hyers stability of the linear differential equation. Rocznik Nauk-Dydakt Prace Mat, 1993, 13:259-270
[13] Obloza M. Connections between Hyers and Lyapunov stability of the ordinary differential equations.Rocznik Nauk-Dydakt Prace Mat, 1997, 14:141-146
[14] Podlubny I. Fractional Differential Equations. San Diego:Academic Press, 1999
[15] Popa D, Rasa I. On the Hyers-Ulam stability of the linear differential equation. J Math Anal Appl, 2011,381:530-537
[16] 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
[17] 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
[18] Wang J, Zhou Y. Mittag-Leffler-Ulam stabilities of fractional evolution equations. Appl Math Lett, 2012,25:723-728
[19] Wang J, Li X. A uniform method to Ulam-Hyers stability for some linear fractional equations. Mediterr J Math, 2016, 13:625-635
[20] 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
[21] Wang C, Xu T Z. Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives. Appl Math, 2015, 60:383-393
[22] Wang C, Xu T Z. Hyers-Ulam stability of differential operators on reproducing kernel function spaces.Complex Anal Oper Theory, 2016, 10:795-813
[23] Wang C, Xu T Z. Hyers-Ulam stability of a class of fractional linear differential equations. Kodai Math J,2015, 38:510-520
[24] Wang C, Xu T Z. Stability of the nonlinear fractional differential equations with the right-sided RiemannLiouville fractional derivative. Discrete Contin Dyn Syst Ser S, 2017, 10:505-521
[25] Xu T Z, Wang C, Rassias T M. On the stability of multi-additive mappings in non-Archimedean normed spaces. J Comput Anal Appl, 2015, 18:1102-1110
[26] Xu T Z. On the stability of multi-Jensen mappings inβ-normed spaces. Appl Math Lett, 2012, 25:1866-1870
[27]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.数学物理学报,2017, 37A(5):846-859Wang C, Xu T Z. Solution and Hyers-Ulam-Rassias stability of a mixed type quadratic-additive functional equation with a parameter in quasi-Banach spaces. Acta Math Sci, 2017, 37A(5):846-859