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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CitationToprakseven, Ş. (2019). The Existence Of Positive Solutıons and a Lyapunov Type Inequality for Boundary Value Problems Of The Fractional Caputo-Fabrizio Differential Equations. Sigma: Journal Of Engineering & Natural Sciences/Mühendislik Ve Fen Bilimleri Dergisi, 37(4).1125-1133.
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.