Home Lyapunov-type inequality for an anti-periodic fractional boundary value problem
Article
Licensed
Unlicensed Requires Authentication

Lyapunov-type inequality for an anti-periodic fractional boundary value problem

  • Rui A. C. Ferreira EMAIL logo
Published/Copyright: February 18, 2017
Become an author with De Gruyter Brill
Author Information Explore this Subject
Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 20 Issue 1

Abstract

In this note we present a Lyapunov-type inequality for a fractional boundary value problem with anti-periodic boundary conditions, that we show to be a generalization of a classical one. Moreover, we address the issue of further research directions for such type of inequalities.

MSC 2010: Primary 34A08; Secondary 26D10; 34L15
Key Words and Phrases: Lyapunov’s inequality; fractional derivatives; boundary value problems; eigenvalues

Acknowledgements

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

References

[1] B. Ahmad, New results for boundary value problems of nonlinear fractional differential equations with non-separated boundary conditions. Acta Math. Vietnam. 36, No 3 (2011), 659–668.Search in Google Scholar

[2] R.C. Brown and D.B. Hinton, Lyapunov inequalities and their applications. In: Survey on Classical Inequalities, Math. Appl. # 51,7 Kluwer Acad. Publ., Dordrecht, 1–25.10.1007/978-94-011-4339-4_1Search in Google Scholar

[3] K.M. Das and A.S. Vatsala, Green’s function for n-n boundary value problem and an analogue of Hartman’s result. J. Math. Anal. Appl. 51, No 3 (1975), 670–677.10.1016/0022-247X(75)90117-1Search in Google Scholar

[4] R.A.C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16, No 4 (2013), 978–984; DOI: 10.2478/s13540-013-0060-5; http://www.degruyter.com/view/j/fca.2013.16.issue-4/issue-files/fca.2013.16.issue-4.xml.DOI: 10.2478/s13540-013-0060-5Search in Google Scholar

[5] R.A.C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J. Math. Anal. Appl. 412, No 2 (2014), 1058–1063.10.1016/j.jmaa.2013.11.025Search in Google Scholar

[6] R.A.C. Ferreira, Some discrete fractional Lyapunov-type inequalities. Fract. Differ. Calc. 5, No 1 (2015), 87–92.10.7153/fdc-05-08Search in Google Scholar

[7] M. Jleli and B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions. Math. Inequal. Appl. 18, No 2 (2015), 443–451.10.7153/mia-18-33Search in Google Scholar

[8] M. Jleli and B. Samet, Lyapunov-type inequalities for fractional boundary-value problems. Electron. J. Differential Equations 2015 (2015), Article ID 88, 11 pp.10.1515/9783110571660-006Search in Google Scholar

[9] M. Jleli, L. Ragoub and B. Samet, A Lyapunov-Type inequality for a fractional differential equation under a Robin boundary condition. J. Funct. Spaces 2015 (2015), Article ID 468536, 5 pp.10.1155/2015/468536Search in Google Scholar

[10] A.M. Lyapunov, Probleme general de la stabilit´e du mouvement, (French Translation of a Russian paper dated 1893). Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27-247; Reprinted as: Ann. Math. Studies, No 17, Princeton, 1947.Search in Google Scholar

[11] D. O’Regan and B. Samet, Lyapunov-type inequalities for a class of fractional differential equations. J. Inequal. Appl. 2015 (2015), Article ID 247, 10 pp.10.1186/s13660-015-0769-2Search in Google Scholar

[12] J.P. Pinasco, Lyapunov-type Inequalities. Springer Briefs in Mathematics, Springer, New York, 2013.10.1007/978-1-4614-8523-0Search in Google Scholar

[13] J. Rong and C. Bai, Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions. Adv. Difference Equ. 2015 (2015), Article ID 82, 10 pp.10.1186/s13662-015-0430-xSearch in Google Scholar

[14] Y. Wang, Lyapunov-type inequalities for certain higher order differential equations with anti-periodic boundary conditions. Appl. Math. Lett. 25, No 12 (2012), 2375-2380.10.1016/j.aml.2012.07.006Search in Google Scholar

Received: 2016-3-13
Published Online: 2017-2-18
Published in Print: 2017-2-1

© 2016 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 20–1–2017)
  4. Survey paper
  5. Ten equivalent definitions of the fractional laplace operator
  6. Research paper
  7. Consensus of fractional-order multi-agent systems with input time delay
  8. Research paper
  9. Asymptotic behavior of solutions of nonlinear fractional differential equations with Caputo-Type Hadamard derivatives
  10. Research paper
  11. A preconditioned fast finite difference method for space-time fractional partial differential equations
  12. Research paper
  13. On existence and uniqueness of solutions for semilinear fractional wave equations
  14. Research paper
  15. Computational solutions of the tempered fractional wave-diffusion equation
  16. Research paper
  17. Completeness on the stability criterion of fractional order LTI systems
  18. Research paper
  19. Wavelet convolution product involving fractional fourier transform
  20. Research paper
  21. Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method
  22. Research paper
  23. A foundational approach to the Lie theory for fractional order partial differential equations
  24. Research paper
  25. Null-controllability of a fractional order diffusion equation
  26. Research paper
  27. New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions
  28. Research paper
  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
  30. Short Paper
  31. Lyapunov-type inequality for an anti-periodic fractional boundary value problem
https://doi.org/10.1515/fca-2017-0015
Keywords for this article
Lyapunov’s inequality; fractional derivatives; boundary value problems; eigenvalues

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 20–1–2017)
  4. Survey paper
  5. Ten equivalent definitions of the fractional laplace operator
  6. Research paper
  7. Consensus of fractional-order multi-agent systems with input time delay
  8. Research paper
  9. Asymptotic behavior of solutions of nonlinear fractional differential equations with Caputo-Type Hadamard derivatives
  10. Research paper
  11. A preconditioned fast finite difference method for space-time fractional partial differential equations
  12. Research paper
  13. On existence and uniqueness of solutions for semilinear fractional wave equations
  14. Research paper
  15. Computational solutions of the tempered fractional wave-diffusion equation
  16. Research paper
  17. Completeness on the stability criterion of fractional order LTI systems
  18. Research paper
  19. Wavelet convolution product involving fractional fourier transform
  20. Research paper
  21. Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method
  22. Research paper
  23. A foundational approach to the Lie theory for fractional order partial differential equations
  24. Research paper
  25. Null-controllability of a fractional order diffusion equation
  26. Research paper
  27. New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions
  28. Research paper
  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
  30. Short Paper
  31. Lyapunov-type inequality for an anti-periodic fractional boundary value problem
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 30.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/fca-2017-0015/html?lang=en
Scroll to top button