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A Lyapunov-type inequality for a fractional boundary value problem

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Abstract

In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this inequality to deduce a criteria for the nonexistence of real zeros of a certain Mittag-Leffler function.

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References

  1. Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, No 2 (2005), 495–505.

    Article  MathSciNet  MATH  Google Scholar 

  2. R.C. Brown, D.B. Hinton, Lyapunov inequalities and their applications. In: Survey on Classical Inequalities (Ed. T.M. Rassias), Math. Appl. 517, Kluwer Acad. Publ., Dordrecht — London (2000), 1–25.

    Chapter  Google Scholar 

  3. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204, Elsevier, Amsterdam (2006).

    Book  MATH  Google Scholar 

  4. A. M. Lyapunov, Probleme général de la stabilité du mouvement, (French Transl. of a Russian paper dated 1893). Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27–247; Reprinted in: Ann. Math. Studies, No. 17, Princeton (1947).

    Google Scholar 

  5. A.M. Nahušev, The Sturm-Liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms. Dokl. Akad. Nauk SSSR 234, No 2 (1977), 308–311.

    MathSciNet  Google Scholar 

  6. A.Yu. Popov, On the number of real eigenvalues of a certain boundaryvalue problem for a second-order equation with fractional derivative. Fundam. Prikl. Mat. 12, No 6 (2006), 137–155; Transl. in J. Math. Sci. (N. York) 151, No 1 (2008), 2726–2740.

    Google Scholar 

  7. M. Rahimy, Applications of fractional differential equations. Appl. Math. Sci. (Ruse) 4, No 49–52 (2010), 2453–2461.

    MathSciNet  MATH  Google Scholar 

  8. A. Tiryaki, Recent developments of Lyapunov-type inequalities. Adv. Dyn. Syst. Appl. 5, No 2 (2010), 231–248.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Lusophone University of Humanities and Technologies, 1749-024, Lisbon, Portugal

    Rui A. C. Ferreira

  2. Center for Research and Development in Mathematics and Applications, 3810-193, Aveiro, Portugal

    Rui A. C. Ferreira

Authors
  1. Rui A. C. Ferreira
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Correspondence to Rui A. C. Ferreira.

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Ferreira, R.A.C. A Lyapunov-type inequality for a fractional boundary value problem. fcaa 16, 978–984 (2013). https://doi.org/10.2478/s13540-013-0060-5

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  • DOI: https://doi.org/10.2478/s13540-013-0060-5

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