Skip to main content

Advertisement

SpringerLink
Log in

Novel Lyapunov-type inequalities for sequential fractional boundary value problems

  • 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 work we derive a Lyapunov-type inequality for a what may be called “sequential fractional right-focal boundary value problem”. A bound for the possible eigenvalues of our problem is also presented.

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. Cabrera, I., Sadarangani, K., Samet, B.: Hartman–Wintner-type inequalities for a class of nonlocal fractional boundary value problems. Math. Methods Appl. Sci. 40(1), 129–136 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dhar, S., Kong, Q., McCabe, M.: Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 2016, 43 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Diethelm, K.: The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, vol. 2004. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  4. Dragomir, S.S., Agarwal, R.P., Barnett, N.S.: Inequalities for beta and gamma functions via some classical and new integral inequalities. J. Inequal. Appl. 5(2), 103–165 (2000)

    MathSciNet  MATH  Google Scholar 

  5. Ferreira, R.A.C.: A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16(4), 978–984 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ferreira, R.A.C.: On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function. J. Math. Anal. Appl. 412(2), 1058–1063 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ferreira, R.A.C.: Lyapunov-type inequalities for some sequential fractional boundary value problems. Adv. Dyn. Syst. Appl. 11(1), 33–43 (2016)

    MathSciNet  Google Scholar 

  8. Ferreira, R.A.C.: Lyapunov-type inequality for an anti-periodic fractional boundary value problem. Fract. Calc. Appl. Anal. 20(1), 284–291 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jleli, M., Samet, B.: Lyapunov-type inequalities for fractional boundary-value problems. Electron. J. Differ. Equ. 2015, 88 (2015)

    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(2), 443–451 (2015)

    MathSciNet  MATH  Google Scholar 

  11. Jleli, M., Kirane, M., Samet, B.: Lyapunov-type inequalities for fractional partial differential equations. Appl. Math. Lett. 66, 30–39 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ma, D.: A generalized Lyapunov inequality for a higher-order fractional boundary value problem. J. Inequal. Appl. 2016, 261 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Podlubny, I.: Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198. Academic Press, San Diego (1999)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grupo Física-Matemática, Faculdade de Ciências, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisbon, Portugal

    Rui A. C. Ferreira

Authors
  1. Rui A. C. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rui A. C. Ferreira.

Additional information

R. A. C. Ferreira was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferreira, R.A.C. Novel Lyapunov-type inequalities for sequential fractional boundary value problems. RACSAM 113, 171–179 (2019). https://doi.org/10.1007/s13398-017-0462-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-017-0462-z

Keywords

Mathematics Subject Classification

Search

Navigation