Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions

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2017_EJQTDE_Jleli_Lyapunow.pdf (453.77 KB)
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URI: http://hdl.handle.net/10347/17587
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2017.1.16

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2017

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Bolyai Institute, University of Szeged
Hungarian Academy of Sciences
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Abstract

New Lyapunov-type inequalities are derived for the fractional boundary value problem Daa u(t) + q(t)u(t) = 0, a <t <b, u(a) = u0(a) = … = u(n-2)(a) = 0, u(b) = Iaa (hu)(b), where n E IN, n > 2, n - 1 < <n, Daa denotes the Riemann–Liouville fractional derivative of order a, Iaa denotes the Riemann–Liouville fractional integral of order a, and q, h 2 C([a, b];R). As an application, we obtain numerical approximations of lower bound for the eigenvalues of corresponding equations

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Lyapunov-type inequality| Fractional boundary value problem| Eigenvalue

Bibliographic citation

Jleli, Mohamed, Nieto, Juan J. and Samet, Bessem: Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions, Electron. J. Qual. Theory Differ. Equ. 2017, No. 16, 1-17.

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The research of J. J. Nieto was partially supported by the Ministerio de Economía y Competitividad of Spain under grant MTM2013-43014-P, co-financed by the European Community fund FEDER, and XUNTA de Galicia under grant GRC2015-004. The third author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia)

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Estatística, Análise Matemática e Optimización