THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS

Year 2019, Volume: 37 Issue: 4, 1129 - 1137, 01.12.2019

Şuayip Toprakseven

Abstract

In this paper, a Lyapunov-type inequality and the existence of the positive solutions for boundary value problems of the nonlinear fractional Caputo-Fabrizio differential equation have been presented. By using the Guo Krasnoselskii’s fixed point theorem on cone and the properties of the associated Green`s function, we prove the existence of the positive solution. Finally, we gave some numerical examples to validate the theoretical findings.

Keywords

Lyapunov-type inequality, fractional Caputo-Fabrizio derivative, Green’s function, positive solution, fixed point.

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