Lyapunov-type inequality and positive solutions for a nonlinear fractional boundary value problem


Kassymov A. Torebek B.T.
February 2025Springer-Verlag Italia s.r.l.

Rendiconti del Circolo Matematico di Palermo
2025#74Issue 1

In this paper, we extend our exploration of a fractional boundary value problem involving left Riemann–Liouville and right Caputo fractional derivatives with order 12<α≤1, as in [13]. Firstly, we investigate the properties of associated Green’s function. Secondly, we prove the existence of positive solutions, where the Guo-Krasnoselskii fixed-point theorem and properties of the Green function play key roles in the proof. Also, we show the generalised Lyapunov and Hartman–Wintner-type inequalities for the associated fractional boundary value problem. Finally, we present some examples for fractional boundary value problems.

Caputo derivative , Hartman–Wintner inequality , Lyapunov inequality , Riemann–Liouville derivative

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Institute of Mathematics and Mathematical Modeling, Shevchenko str., 28, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis

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