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Year 2019, Volume: 7 Issue: 2, 264 - 267, 15.10.2019

Abstract

References

  • [1] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. 27(1941), 222-224.
  • [2] R. W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math., 23, (5), (2012), 9 pp.
  • [3] R. W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstr. Appl. Anal., 2012, (2012), 1-8.
  • [4] R. W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstr. Appl. Anal., 2012, (2012), 1-10.
  • [5] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Stydies, 204, Elsevier Science, B. V., Amsterdam, 2006.
  • [6] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equa- tions, John wiley, New York, 1993.
  • [7] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [8] Sh. Peng and J. R.Wang, Existence and Ulam-Hyers stability of ODEs involving two Caputo fractional derivatives, Electronic Journal of Qualitative Theory of Differential Equations, 48-54 (52), (2015), 1-16.
  • [9] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, (1978), 297-300.
  • [10] S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Science eds., Wiley, New York, 1960.
  • [11] J. Wang and X. Li, Ulam-Hyers stability of fractional Langevin equations, Appl. Math. Comput., 258, (2015), 72-83.
  • [12] J. Wang and Z. Lin, Ulam's type stability of Hadamard type fractional integral equations, Filomat, 28 (7), (2014), 1323-1331.
  • [13] J. Wang and Z. Lin, A class of impulsive nonautonomous differential equations and Ulam- Hyers-Rassias stability, Mathematical Methods in the Applied Sciences, 38 (5), (2015), 865-880.
  • [14] J. R.Wang, L. Lv and Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron. J. Qual. Theory Differ. Equ., 63, (2011), 1-10.
  • [15] J. R.Wang, L. Lv and Y. Zhou, New concepts and results in stability of fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat. 17, (2012), 2530-2538.
  • [16] J. R. Wang and Y. Zhang, Ulam-Hyers-Mittag-Leffler stability of fractional-order delay differential equations, Optimization: A Journal of Mathematical Programming and opti- mization Research, 63 (8), (2014), 1181-1190.
  • [17] J. R.Wang, Y. Zhou and M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Appl. Math. Comput., 64, (2012), 3389-3405.
  • [18] J. R.Wang, Y. Zhou and Z. Lin, On a new class of impulsive fractional differential equations, App. Math. Comput., 242, (2014), 649-657.
  • [19] W. Wei, Xuezhu. Li and Xia Li, New stability results for fractional integral equation, Com- put. Math. Appl., 64 (10), (2012), 3468-3476.
  • [20] H. M. Srivastava, Y. Ling and G. Bao, Some distortion inequalities associated with the fractional derivatives of analytic and univalent functions, J .Ineq. Pure Appl. Math ., 2, (2001), 1-6.

Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk

Year 2019, Volume: 7 Issue: 2, 264 - 267, 15.10.2019

Abstract

In this paper, we prove the Mittag-Leffler-Hyers-Ulam stability of Cauchy fractional differential equations in the unit disk for the linear and non-linear cases.

References

  • [1] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. 27(1941), 222-224.
  • [2] R. W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math., 23, (5), (2012), 9 pp.
  • [3] R. W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstr. Appl. Anal., 2012, (2012), 1-8.
  • [4] R. W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstr. Appl. Anal., 2012, (2012), 1-10.
  • [5] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Stydies, 204, Elsevier Science, B. V., Amsterdam, 2006.
  • [6] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equa- tions, John wiley, New York, 1993.
  • [7] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [8] Sh. Peng and J. R.Wang, Existence and Ulam-Hyers stability of ODEs involving two Caputo fractional derivatives, Electronic Journal of Qualitative Theory of Differential Equations, 48-54 (52), (2015), 1-16.
  • [9] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, (1978), 297-300.
  • [10] S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Science eds., Wiley, New York, 1960.
  • [11] J. Wang and X. Li, Ulam-Hyers stability of fractional Langevin equations, Appl. Math. Comput., 258, (2015), 72-83.
  • [12] J. Wang and Z. Lin, Ulam's type stability of Hadamard type fractional integral equations, Filomat, 28 (7), (2014), 1323-1331.
  • [13] J. Wang and Z. Lin, A class of impulsive nonautonomous differential equations and Ulam- Hyers-Rassias stability, Mathematical Methods in the Applied Sciences, 38 (5), (2015), 865-880.
  • [14] J. R.Wang, L. Lv and Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron. J. Qual. Theory Differ. Equ., 63, (2011), 1-10.
  • [15] J. R.Wang, L. Lv and Y. Zhou, New concepts and results in stability of fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat. 17, (2012), 2530-2538.
  • [16] J. R. Wang and Y. Zhang, Ulam-Hyers-Mittag-Leffler stability of fractional-order delay differential equations, Optimization: A Journal of Mathematical Programming and opti- mization Research, 63 (8), (2014), 1181-1190.
  • [17] J. R.Wang, Y. Zhou and M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Appl. Math. Comput., 64, (2012), 3389-3405.
  • [18] J. R.Wang, Y. Zhou and Z. Lin, On a new class of impulsive fractional differential equations, App. Math. Comput., 242, (2014), 649-657.
  • [19] W. Wei, Xuezhu. Li and Xia Li, New stability results for fractional integral equation, Com- put. Math. Appl., 64 (10), (2012), 3468-3476.
  • [20] H. M. Srivastava, Y. Ling and G. Bao, Some distortion inequalities associated with the fractional derivatives of analytic and univalent functions, J .Ineq. Pure Appl. Math ., 2, (2001), 1-6.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nasrin Eghbali

Vida Kalvandi This is me

Publication Date October 15, 2019
Submission Date December 27, 2017
Acceptance Date July 8, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Eghbali, N., & Kalvandi, V. (2019). Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk. Konuralp Journal of Mathematics, 7(2), 264-267.
AMA Eghbali N, Kalvandi V. Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk. Konuralp J. Math. October 2019;7(2):264-267.
Chicago Eghbali, Nasrin, and Vida Kalvandi. “Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 264-67.
EndNote Eghbali N, Kalvandi V (October 1, 2019) Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk. Konuralp Journal of Mathematics 7 2 264–267.
IEEE N. Eghbali and V. Kalvandi, “Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk”, Konuralp J. Math., vol. 7, no. 2, pp. 264–267, 2019.
ISNAD Eghbali, Nasrin - Kalvandi, Vida. “Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk”. Konuralp Journal of Mathematics 7/2 (October 2019), 264-267.
JAMA Eghbali N, Kalvandi V. Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk. Konuralp J. Math. 2019;7:264–267.
MLA Eghbali, Nasrin and Vida Kalvandi. “Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 264-7.
Vancouver Eghbali N, Kalvandi V. Mittag-Leffler-Hyers-Ulam Stability for Cauchy Fractional Differential Equation in the Unit Disk. Konuralp J. Math. 2019;7(2):264-7.
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