References
- [1] S. M. Ulam, A collection of the mathematical problems, Interscience Publ., New York, 1960.
- [2] J. Wang, M. Feckan,Y. Zhou, Ulam’s type stability of impulsive ordinary differential equations, J. Math. Anal. Appl. 395 (2012), 258-264.
- [3] S.M. Jung, J. Brzdek, Hyers-Ulam stability of the delay equation yʹ(t) = y(t - τ), Abstr. Appl. Anal.(2010) 88 Article ID 372176,10 pages.
- [4] S. M. Jung, A fixed point approach to the stability of linear differential yʹ = f(x; y), Bull. Malays. Math. Sci. Soc. 33 (2) (2010), 47-56.
- [5] S.M. Jung, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 17 (2004), 1135-1140.
- [6] M. Gachpazan, O. Baghani, Hyers-Ulam stability of nonlinear integral equation, Fixed Point Theory and Applications Volume (2010) Article ID 927640, 6 pages.
- [7] D. Otrocol, V. Ilea, Ulam stability for a delay differential equation, Cent. Eur. J. Math. 11(7) ( 2013), 1296-1303.
- [8] Y. Li, Y. Shen, Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett. 23 (2010), 306-309.
- [9] J. Huang, S. M. Jung,Y. Li, Hyers-Ulam stability of nonlinear differential equations, Bull,Korean Math.Soc. 43 (2006), 107-117.
- [10] J. Huang, Y. Li, Hyers-Ulam stability of delay differential equations of first order, Math. Nachr.(2015), 1-7.
- [11] J. Wang,L. Lv,Y. Zhou, New concepts and results in stability of fractional differential equations, Commun Nonlinear Sci Numer Simulat 17 (2012), 2530-2538.
- [12] J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Qualit Th Diff Equat 63 (2011), 1-10.
- [13] J.Wang, X. Li, Eα-Ulam type stability of fractional order ordinary differential equations, J. Appl. Math. Comput. 45 (2014), 449-459.
- [14] J. Wang, Y. Zhanga, Ulam-Hyers-Mittag-Leffler stability of fractional-order delay differential equations, Optimization 64 (8) (2014), 1181-1190.
- [15] N. Eghbali, V. Kalvandi, J. M. Rassias, A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation, Open Math. 14 (2016), 237-246.
- [16] Wei Wei, Xuezhu Li, Xia Li, New stability results for fractional integral equations, Computers and Mathematics with Applications 64 (2012), 3468-3476.
- [17] M. Benchohra, M. Said Souid, Integrable solutions for implicit fractional order differential equations, TJMM, 6 (2) (2014), 101-107.
- [18] M. Benchohra, J. Lazreg, On stability for nonlinear implicit fractional differential equations, Le Matematiche Vol. LXX (2015) Fasc. II, 49-61.
- [19] M. Benchohraa, S. Bouriaha, Existence and stability results for nonlinear boundary value problem for implicit differential equations of fractional order, Moroccan J. Pure and Appl. Anal., 1(1) (2015), 22-37.
- [20] K. D. Kucche, J. J. Nieto, V. Venktesh, Theory of nonlinear implicit fractional differential equations, Differ. Equ. Dyn. Syst. DOI 10.1007/s12591-016-0297-7.
- [21] S.T.Sutar, K.D.Kucche, Global existence and uniqueness for implicit differential equations of arbitrary order, Fractional Differential Calculus 5(2)(2015), 199-208.
- [22] K. S. Miller, B. Ross, An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993.
- [23] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
- [24] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
- [25] K. Diethelm, The analysis of fractional differential equations, Lecture Notes in Mathematics, Springer-verlag; Berlin, Heidelberg, 2010.
- [26] Michalski MW, Derivatives of noninteger order and their applications, Dissertationes Mathematicae.Polska Akademia Nauk.,Instytut Matematyczny,Warszawa;1993.
- [27] H. Ye, J. Gao, Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation, J. Math. Anal. Appl., 328 (2007), 1075-1081.
- [28] A. H. Siddiqi, Functional analysis with applications, Tata McGraw-Hill Publishing ltd , New Delhi, 1986.