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Laplace transform method for the Ulam stability of linear fractional differential equations with constant coefficients. (English) Zbl 1366.34011
Summary: Using the Laplace transform method, this paper deals with the Ulam stability of linear fractional differential equations with constant coefficients.

##### MSC:
 34A08 Fractional ordinary differential equations and fractional differential inclusions 44A10 Laplace transform 34A30 Linear ordinary differential equations and systems, general 34D10 Perturbations of ordinary differential equations
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##### References:
 [1] Alsina, C; Ger, R, On some inequalities and stability results related to the exponential function, J. Inequal. Appl., 2, 373-380, (1998) · Zbl 0918.39009 [2] Jiang, JF; Cao, DQ; Chen, HT, The fixed point approach to the stability of fractional differential equations with causal operators, Qual. Theory Dyn. Syst., 15, 3-18, (2016) · Zbl 1343.34016 [3] Jung, SM, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 17, 1135-1140, (2004) · Zbl 1061.34039 [4] Jung, SM, Hyers-Ulam stability of linear differential equations of first order (III), J. Math. Anal. Appl., 311, 139-146, (2005) · Zbl 1087.34534 [5] Jung, S.M.: Legendre’s differential equation and its Hyers-Ulam stability. Abstr. Appl. Anal. 2007, 14 (Article ID 56419) · Zbl 1153.34306 [6] Jung, SM, A fixed point approach to the stability of differential equations $$y^{′ }=F(x, y)$$, Bull. Malays. Math. Sci. Soc., 33, 47-56, (2010) · Zbl 1184.26012 [7] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) · Zbl 1092.45003 [8] Miura, T; Takahasi, SE; Choda, H, On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo J. Math., 24, 467-476, (2001) · Zbl 1002.39039 [9] Miura, T, On the Hyers-Ulam stability of a differentiable map, Sci. Math. Jpn., 55, 17-24, (2002) · Zbl 1025.47041 [10] Miura, T; Miyajima, S; Takahasi, SE, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl., 286, 136-146, (2003) · Zbl 1045.47037 [11] Obloza, M, Hyers stability of the linear differential equation, Rocznik Nauk. Dydakt. Prace Mat., 13, 259-270, (1993) · Zbl 0964.34514 [12] Rezaei, H; Jung, SM; Rassias, TM, Laplace transform and Hyers-Ulam stability of linear differential equations, J. Math. Anal. Appl., 403, 244-251, (2013) · Zbl 1286.34077 [13] Takahasi, SE; Miura, T; Miyajima, S, On the Hyers-Ulam stability of the Banach space-valued differential equation $$y^{′ }=λ {y}$$, Bull. Korean Math. Soc., 39, 309-315, (2002) · Zbl 1011.34046 [14] Takahasi, SE; Takagi, H; Miura, T; Miyajima, S, The Hyers-Ulam stability constants of first order linear differential operators, J. Math. Anal. Appl., 296, 403-409, (2004) · Zbl 1074.47022 [15] Wang, GW; Zhou, MR; Sun, L, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 21, 1024-1028, (2008) · Zbl 1159.34041 [16] Wang, JR; Lv, LL; Zhou, Y, New concepts and results in stability of fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17, 2530-2538, (2012) · Zbl 1252.35276 [17] Wang, JR; Zhou, M; Fečkan, M, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl., 64, 3389-3405, (2012) · Zbl 1268.34033 [18] Wang, JR; Fečkan, M; Zhou, M, Presentation of solutions of impulsive fractional Langevin equations and existence results, Eur. Phys. J. Spec. Top., 222, 1855-1872, (2013) [19] Wang, JR; Li, XZ, $$E_{α }$$-Ulam type stability of fractional order ordinary differential equations, J. Appl. Math. Comput., 45, 449-459, (2014) · Zbl 1296.34035 [20] Wang, JR; Li, XZ, Ulam-Hyers stability of fractional Langevin equations, Appl. Math. Comput., 258, 72-83, (2015) · Zbl 1338.39047 [21] Wang, JR; Li, XZ, A uniform method to Ulam-Hyers stability for some linear fractional equations, Mediterr. J. Math., 13, 625-635, (2016) · Zbl 1337.26020 [22] Wei, W; Li, XZ; Li, X, New stability for fractional integral equation, Comput. Math. Appl., 64, 3468-3476, (2012) · Zbl 1268.45007 [23] Ulam, S.M.: Problems in Modern Mathematics. Wiley, New York (1960) · Zbl 0137.24201
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