THE EXISTENCE of POSITIVE SOLUTIONS and A LYAPUNOV TYPE INEQUALITY for BOUNDARY VALUE PROBLEMS of the FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS
Sigma Journal of Engineering and Natural Sciences, cilt.37, sa.4, ss.1129-1137, 2019 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 37 Sayı: 4
- Basım Tarihi: 2019
- Dergi Adı: Sigma Journal of Engineering and Natural Sciences
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.1129-1137
- Anahtar Kelimeler: fixed point, fractional Caputo-Fabrizio derivative, Green’s function, Lyapunov-type inequality, positive solution
- Yozgat Bozok Üniversitesi Adresli: Evet
Özet
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.