Lyapunov-type inequalities for a nonlinear fractional boundary value problem

Kassymov A. Torebek B.T.
1 January 2021 Springer-Verlag Italia s.r.l.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
2021 #115 Issue 1

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 < α≤ 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 α= 1 , our results coincide with the classical Lyapunov and Hartman–Wintner inequalities, respectively.

Caputo derivative , Fractional hybrid equation , Hartman–Wintner inequality , Lyapunov inequality , Riemann–Liouville derivative

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Al–Farabi Kazakh National University, Al–Farabi Ave. 71, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
RUDN University, 6 Miklukho-Maklay Street, Moscow, 117198, Russian Federation

Al–Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
RUDN University

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