Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

Chun Wang1, Tianzhou Xu2
1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China
2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Tóm tắt

Từ khóa


Tài liệu tham khảo

S. András, A. R. Mészáros: Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219 (2013), 4853–4864.

M. Eshaghi Gordji, Y. J. Cho, M. B. Ghaemi, B. Alizadeh: Stability of the second order partial differential equations. J. Inequal. Appl. (electronic only) 2011 (2011), Article ID 81, 10 pages.

B. Hegyi, S.-M. Jung: On the stability of Laplace’s equation. Appl. Math. Lett. 26 (2013), 549–552.

R. W. Ibrahim: Ulam stability of boundary value problem. Kragujevac J. Math. 37 (2013), 287–297.

S.-M. Jung: Hyers-Ulam stability of linear differential equations of first order. Appl. Math. Lett. 17 (2004), 1135–1140.

S.-M. Jung: Hyers-Ulam stability of linear differential equations of first order. III. J. Math. Anal. Appl. 311 (2005), 139–146.

S.-M. Jung: Hyers-Ulam stability of linear differential equations of first order. II. Appl. Math. Lett. 19 (2006), 854–858.

A. A. Kilbas, H. M. Srivastava, J. J. Trujillo: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204, Elsevier, Amsterdam, 2006.

N. Lungu, D. Popa: Hyers-Ulam stability of a first order partial differential equation. J. Math. Anal. Appl. 385 (2012), 86–91.

D. Popa, I. Raşa: On the Hyers-Ulam stability of the linear differential equation. J. Math. Anal. Appl. 381 (2011), 530–537.

H. Rezaei, S.-M. Jung, T. M. Rassias: Laplace transform and Hyers-Ulam stability of linear differential equations. J. Math. Anal. Appl. 403 (2013), 244–251.

J. Wang, L. Lv, Y. Zhou: New concepts and results in stability of fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 2530–2538.

J. Wang, Y. Zhang: A class of nonlinear differential equations with fractional integrable impulses. Commun. Nonlinear Sci. Numer. Simul. 19 (2014), 3001–3010.

J. Wang, Y. Zhou: Mittag-Leffler-Ulam stabilities of fractional evolution equations. Appl. Math. Lett. 25 (2012), 723–728.