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Lyapunov-type inequalities for a nonlinear fractional boundary value problem

Aidyn Kassymov (UGent) and Berikbol Torebek (UGent)
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Abstract
In this paper, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a nonlinear fractional hybrid equation with left Riemann-Liouville and right Caputo fractional derivatives of order 1/2 < alpha <= 1, subject to Dirichlet boundary conditions. It is also shown that failure of the Lyapunov-type and Hartman-Wintner-type inequalities, corresponding nonlinear boundary value problem has only trivial solutions. In the case alpha = 1, our results coincide with the classical Lyapunov and Hartman-Wintner inequalities, respectively.
Keywords
Geometry and Topology, Algebra and Number Theory, Applied Mathematics, Analysis, Computational Mathematics, Lyapunov inequality, Hartman-Wintner inequality, Fractional hybrid equation, Caputo derivative, Riemann-Liouville derivative

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MLA
Kassymov, Aidyn, and Berikbol Torebek. “Lyapunov-Type Inequalities for a Nonlinear Fractional Boundary Value Problem.” REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol. 115, no. 1, 2020, doi:10.1007/s13398-020-00954-9.
APA
Kassymov, A., & Torebek, B. (2020). Lyapunov-type inequalities for a nonlinear fractional boundary value problem. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 115(1). https://doi.org/10.1007/s13398-020-00954-9
Chicago author-date
Kassymov, Aidyn, and Berikbol Torebek. 2020. “Lyapunov-Type Inequalities for a Nonlinear Fractional Boundary Value Problem.” REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 115 (1). https://doi.org/10.1007/s13398-020-00954-9.
Chicago author-date (all authors)
Kassymov, Aidyn, and Berikbol Torebek. 2020. “Lyapunov-Type Inequalities for a Nonlinear Fractional Boundary Value Problem.” REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 115 (1). doi:10.1007/s13398-020-00954-9.
Vancouver
1.
Kassymov A, Torebek B. Lyapunov-type inequalities for a nonlinear fractional boundary value problem. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS. 2020;115(1).
IEEE
[1]
A. Kassymov and B. Torebek, “Lyapunov-type inequalities for a nonlinear fractional boundary value problem,” REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol. 115, no. 1, 2020.
@article{8713192,
  abstract     = {{In this paper, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a nonlinear fractional hybrid equation with left Riemann-Liouville and right Caputo fractional derivatives of order 1/2 < alpha <= 1, subject to Dirichlet boundary conditions. It is also shown that failure of the Lyapunov-type and Hartman-Wintner-type inequalities, corresponding nonlinear boundary value problem has only trivial solutions. In the case alpha = 1, our results coincide with the classical Lyapunov and Hartman-Wintner inequalities, respectively.}},
  articleno    = {{15}},
  author       = {{Kassymov, Aidyn and Torebek, Berikbol}},
  issn         = {{1578-7303}},
  journal      = {{REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS}},
  keywords     = {{Geometry and Topology,Algebra and Number Theory,Applied Mathematics,Analysis,Computational Mathematics,Lyapunov inequality,Hartman-Wintner inequality,Fractional hybrid equation,Caputo derivative,Riemann-Liouville derivative}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{10}},
  title        = {{Lyapunov-type inequalities for a nonlinear fractional boundary value problem}},
  url          = {{http://dx.doi.org/10.1007/s13398-020-00954-9}},
  volume       = {{115}},
  year         = {{2020}},
}

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