Skip to main content

Advertisement

SpringerLink
Log in

Lyapunov type inequalities for a fractional thermostat model

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we present some Lyapunov-type inequalities for a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lyapunov, A.M.: Probléme général de la stabilité du mouvement. Ann. Fac. Sci. Univ. Tolouse 2, 203–407 (1907)

    Google Scholar 

  2. Hartman, P., Wintner, A.: On an oscillation criterion of Lyapunov. Am. J. Math. 73, 885–890 (1951)

    Article  MATH  Google Scholar 

  3. Brown, R.C., Hilton, D.B.: Opial’ inequality and oscillation of 2nd order equations. Proc. Am. Math. Soc. 125, 1123–1129 (1997)

    Article  MathSciNet  Google Scholar 

  4. Çakmak, D.: Lyapunov-type integral inequalities for certain higher order differential equations. Appl. Math. Comput. 216, 368–373 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Lee, C., Yeh, C., Hong, C., Argarwal, R.P.: Lyapunov and Wirtinger inequalities. Appl. Math. Lett. 17, 847–853 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pachpatte, B.G.: On Lyapunov-type inequalities for certain higher order differential equations. J. Math. Anal. Appl. 195, 527–536 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yang, X., Lo, K.: Lyapunov-type inequality for a class of even-order differential equations. Appl. Math. Comput. 215, 3884–3890 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Ferreira, R.A.C.: A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16, 978–984 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ferreira, R.A.C.: On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J. Math. Anal. Appl. 412, 1058–1063 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jleli, M., Samet, B.: Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions. Math. Inequal. Appl. 18, 443–451 (2015)

    MathSciNet  MATH  Google Scholar 

  11. O’Regan, D., Samet, B.: Lyapunov-type inequalities for a class of fractional differential equations. J. Inequal. Appl. 2015, 247 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rong, J., Bai, C.: Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions. Adv. Differ. Eq. 2015, 82 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Guidotti, P., Merino, S.: Gradual loss of positivity and hidden invariant cones in a scalar heat equation. Diff. Integr. Equ. 13, 1551–1568 (2000)

    MathSciNet  MATH  Google Scholar 

  14. 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)

    Google Scholar 

  15. Podlubny, I.: Fractional Differential Equations. Academic, San Diego (1999)

    MATH  Google Scholar 

  16. Nieto, J.J., Pimentel, J.: Positive solutions of a fractional thermostat model. Bound. Value Probl. 2013, 5 (2013)

Download references

Acknowledgements

The third author was partially supported by the Project MTM 2013–44357–P.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017, Las Palmas de Gran Canaria, Spain

    I. J. Cabrera, J. Rocha & K. B. Sadarangani

Authors
  1. I. J. Cabrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. B. Sadarangani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. B. Sadarangani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cabrera, I.J., Rocha, J. & Sadarangani, K.B. Lyapunov type inequalities for a fractional thermostat model. RACSAM 112, 17–24 (2018). https://doi.org/10.1007/s13398-016-0362-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-016-0362-7

Keywords

Mathematics Subject Classification

Search

Navigation