References

HYERS-ULAM STABILITY OF A NONLINEAR MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATION ON BOUNDED TIME INTERVAL


[1] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

[2] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John, Wiley, 1993.

[3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

[4] M. Obloza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. 13 (1993), 259-270.

[5] C. Alsina and R. Ger, On some inequalities and stability results related to the exponential function, Journal of Inequalities and Applications 2(4) (1998), 373-380.

[6] T. Miura, On the Hyers-Ulam stability of a differentiable map, Scientiae Mathematicae Japonicae 55(1) (2002), 17-24.

[7] T. Miura, S. E. Takahasi and H. Choda, On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo Journal of Mathematics 24(2) (2001), 467-476.
DOI: https://doi.org/10.3836/tjm/1255958187

[8] S. E. Takahasi, H. Takagi, T. Miura and S. Miyajima, The Hyers-Ulam stability constants of first order linear differential operators, Journal of Mathematical Analysis and Applications 296(2) (2004), 403-409.
DOI: https://doi.org/10.1016/j.jmaa.2003.12.044

[9] M. Obloza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. 14 (1997), 141-146.

[10] S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, Applied Mathematics Letters 17(10) (2004), 1135-1140.
DOI: https://doi.org/10.1016/j.aml.2003.11.004

[11] S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, III, Journal of Mathematical Analysis and Applications 311(1) (2005), 139-146.
DOI: https://doi.org/10.1016/j.jmaa.2005.02.025

[12] S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, II, Applied Mathematics Letters 19(9) (2006), 854-858.
DOI: https://doi.org/10.1016/j.aml.2005.11.004

[13] J. Wang, L. Lv and Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electronic Journal of Qualitative Theory of Differential Equations 63 (2011), 1-10.
DOI: https://doi.org/10.14232/ejqtde.2011.1.63

[14] J. Wang, L. Lv and Y. Zhou, New concepts and results in stability of fractional differential equations, Communications in Nonlinear Science and Numerical Simulation 17(6) (2012), 2530-2538.
DOI: https://doi.org/10.1016/j.cnsns.2011.09.030

[15] C. Wang and T. Z. Xu, Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives, Applications of Mathematics 60(4) (2015), 383-393.
DOI: https://doi.org/10.1007/s10492-015-0102-x

[16] Mohamed I. Abbas, Ulam stability of fractional impulsive differential equations with Riemann-Liouville integral boundary conditions, Journal of Contemporary Mathematical Analysis 50(5) (2015), 209-219.
DOI: https://doi.org/10.3103/S1068362315050015

[17] J. Wang, Y. Zhou and Michal Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Computers & Mathematics with Applications 64(10) (2012), 3389-3405.
DOI: https://doi.org/10.1016/j.camwa.2012.02.021

[18] Z. P. Yang, T. Z. Xu and M. Qi, Ulam-Hyers stability for fractional differential equations in quaternionic analysis, Advances in Applied Clifford Algebras 26(1) (2016), 469-478.
DOI: https://doi.org/10.1007/s00006-015-0576-3

[19] N. Eghbali, V. Kalvandi and J. M. Rassias, A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation, Open Mathematics 14(1) (2016), 237-246.
DOI: https://doi.org/10.1515/math-2016-0019

[20] R. W. Ibrahim and H. A. Jalab, Existence of Ulam stability for iterative fractional differential equations based on fractional entropy, Entropy 17(5) (2015), 3172-3181.
DOI: https://doi.org/10.3390/e17053172

[21] Y. H. Shen and W. Chen, Laplace transform method for the Ulam stability of linear fractional differential equations with constant coefficients, Mediterranean Journal of Mathematics 14(1) (2017), 1-17.
DOI: https://doi.org/10.1007/s00009-016-0835-0

[22] J. F. Jiang, D. Q. Cao and H. T. Chen, The fixed point approach to the stability of fractional differential equations with causal operators, Qualitative Theory of Dynamical Systems 15(1) (2016), 3-18.
DOI: https://doi.org/10.1007/s12346-015-0136-1