Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2014

01.06.2014 | Original Research

E α -Ulam type stability of fractional order ordinary differential equations

verfasst von: JinRong Wang, Xuezhu Li

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, the concepts of \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability, generalized \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability, \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability and generalized \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability for fractional order ordinary differential equations are raised. Without loss of generality, \(\mathbb{E}_{\alpha}\)-Ulam-Hyers-Rassias stability result is derived by using a singular integral inequality of Gronwall type. Two examples are also provided to illustrate our results.
Vorheriger Artikel On the entropy of LEGO ®
Nächster Artikel Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
András, S., Kolumbán, J.J.: On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions. Nonlinear Anal. 82, 1–11 (2013) CrossRefMATHMathSciNet
2.
András, S., Mészáros, A.R.: Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219, 4853–4864 (2013) CrossRefMathSciNet
3.
4.
Cădariu, L.: Stabilitatea Ulam-Hyers-Bourgin Pentru Ecuatii Functionale. Univ. Vest Timişoara, Timişara (2007)
5.
6.
Deng, W.: Smoothness and stability of the solutions for nonlinear fractional differential equations. Nonlinear Anal. 72, 1768–1777 (2010) CrossRefMATHMathSciNet
7.
Diethelm, K.: The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics. Springer, New York (2010) CrossRefMATH
8.
9.
Hyers, D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941) CrossRefMathSciNet
10.
Hyers, D.H., Isac, G., Rassias, T.M.: Stability of Functional Equations in Several Variables. Birkhäuser, Basel (1998) CrossRefMATH
11.
Jung, S.M.: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor (2001) MATH
12.
13.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006) CrossRefMATH
14.
Lakshmikantham, V., Leela, S., Devi, J.V.: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge (2009) MATH
15.
Li, Y., Chen, Y., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45, 1965–1969 (2009) CrossRefMATHMathSciNet
16.
Li, Y., Chen, Y., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59, 1810–1821 (2010) CrossRefMATHMathSciNet
17.
Lungu, N., Popa, D.: Hyers-Ulam stability of a first order partial differential equation. J. Math. Anal. Appl. 385, 86–91 (2012) CrossRefMATHMathSciNet
18.
Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993) MATH
19.
Miura, T., Miyajima, S., Takahasi, S.E.: A characterization of Hyers-Ulam stability of first order linear differential operators. J. Math. Anal. Appl. 286, 136–146 (2003) CrossRefMATHMathSciNet
20.
Miura, T., Miyajima, S., Takahasi, S.E.: Hyers-Ulam stability of linear differential operator with constant coefficients. Math. Nachr. 258, 90–96 (2003) CrossRefMATHMathSciNet
21.
Obłoza, M.: Hyers stability of the linear differential equation. Rocz. Nauk.-Dydakt. Pr. Mat. 13, 259–270 (1993) MATH
22.
Obłoza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocz. Nauk.-Dydakt. Pr. Mat. 14, 141–146 (1997) MATH
23.
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) MATH
24.
Rassias, T.M.: On the stability of linear mappings in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978) CrossRefMATH
25.
26.
27.
Rus, I.A.: Ulam stability of ordinary differential equations. Stud. Univ. Babes,-Bolyai, Math. 54, 125–133 (2009) MATHMathSciNet
28.
Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpath. J. Math. 26, 103–107 (2010) MATHMathSciNet
29.
Takahasi, S.E., Miura, T., Miyajima, S.: On the Hyers-Ulam stability of the Banach space-valued differential equation y′=λy. Bull. Korean Math. Soc. 39, 309–315 (2002) CrossRefMATHMathSciNet
30.
Tarasov, V.E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer & HEP, Berlin (2011)
31.
Ulam, S.M.: A Collection of Mathematical Problems. Interscience Publishers, New York (1968)
32.
Wang, J., Lv, L., Zhou, Y.: Ulam stability and data dependence for fractional differential equations with Caputo derivative. Electron. J. Qual. Theory Differ. Equ. 63, 1–10 (2011) CrossRefMathSciNet
33.
Wang, R.N., Chen, D.H., Xiao, T.J.: Abstract fractional Cauchy problems with almost sectorial operators. J. Differ. Equ. 252, 202–235 (2012) CrossRefMATHMathSciNet
34.
Wang, J., Fec̆kan, M., Zhou, Y.: Ulam’s type stability of impulsive ordinary differential equations. J. Math. Anal. Appl. 395, 258–264 (2012) CrossRefMATHMathSciNet
35.
Wang, J., Lv, L., Zhou, Y.: New concepts and results in stability of fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 2530–2538 (2012) CrossRefMATHMathSciNet
36.
Wang, J., Zhou, Y., Fec̆kan, M.: Nonlinear impulsive problems for fractional differential equations and Ulam stability. Comput. Math. Appl. 64, 3389–3405 (2012) CrossRefMATHMathSciNet
37.
Wang, J., Fec̆kan, M., Zhou, Y.: Presentation of solutions of impulsive fractional Langevin equations and existence results. Eur. Phys. J. Spec. Top. 222, 1857–1874 (2013) CrossRef
38.
Ye, H., Gao, J., Ding, Y.: A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328, 1075–1081 (2007) CrossRefMATHMathSciNet
39.
Zhou, Y., Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal., Real World Appl. 11, 4465–4475 (2010) CrossRefMATHMathSciNet
Metadaten
Titel
E α -Ulam type stability of fractional order ordinary differential equations
verfasst von
JinRong Wang
Xuezhu Li
Publikationsdatum
01.06.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2014
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-013-0731-8

Weitere Artikel der Ausgabe 1-2/2014

Journal of Applied Mathematics and Computing 1-2/2014 Zur Ausgabe

Original Research

Positive solutions for a high-order semipositone fractional differential equation with integral boundary conditions

Original Research

Viscosity iteration algorithms for nonlinear variational inclusions and fixed point problems in Banach spaces

Original Research

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Original Research

An impulsive periodic predator-prey Lotka–Volterra type dispersal system with mixed functional responses

Original Research

Extremal values of augmented eccentric connectivity index of V-phenylenic nanotorus

Original Research

On the entropy of LEGO ®

Premium Partner

    Bildnachweise