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

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Sigma Mühendislik ve Fen Bilimleri Dergisi
Volume:37 Issue:4
THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF TH...

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

Authors : Şuayip TOPRAKSEVEN

Pages : 1129-1137

View : 44 | Download : 9

Publication Date : 2019-12-01

Article Type : Research Paper

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, Greens function, positive solution, fixed point

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