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Fractional Calculus and Applied Analysis

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A Lyapunov-type inequality for a fractional boundary value problem

Rui Ferreira
  • Department of Mathematics, Lusophone University of Humanities and Technologies, 1749-024, Lisbon, Portugal
  • Center for Research and Development in Mathematics and Applications, 3810-193, Aveiro, Portugal
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Published Online: 2013-09-13 | DOI: https://doi.org/10.2478/s13540-013-0060-5

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.

MSC: Primary: 34A08, 34A40; Secondary: 26D10, 34C10, 33E12

Keywords: Lyapunov’s inequality; fractional derivative, Green’s function; Mittag-Leffler function

  • [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. http://dx.doi.org/10.1016/j.jmaa.2005.02.052CrossrefGoogle 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. http://dx.doi.org/10.1007/978-94-011-4339-4_1CrossrefGoogle 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). http://dx.doi.org/10.1016/S0304-0208(06)80001-0CrossrefGoogle 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. 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. Google Scholar

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

About the article

Published Online: 2013-09-13

Published in Print: 2013-12-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0060-5.

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© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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