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 \(1/2<\alpha \le 1,\) 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.
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Acknowledgements
The authors would like to thank to the reviewers for their valuable comments and remarks. This research is financially supported by the FWO Odysseus 1 grant G.0H94.18N:Analysis and Partial Differential Equations and by the “5–100” program of RUDN University.
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Kassymov, A., Torebek, B.T. Lyapunov-type inequalities for a nonlinear fractional boundary value problem. RACSAM 115, 15 (2021). https://doi.org/10.1007/s13398-020-00954-9
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DOI: https://doi.org/10.1007/s13398-020-00954-9
Keywords
- Lyapunov inequality
- Hartman–Wintner inequality
- Fractional hybrid equation
- Caputo derivative
- Riemann–Liouville derivative