THE EXISTENCE of POSITIVE SOLUTIONS and A LYAPUNOV TYPE INEQUALITY for BOUNDARY VALUE PROBLEMS of the FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS

Toprakseven Ş.

Sigma Journal of Engineering and Natural Sciences, cilt.37, sa.4, ss.1129-1137, 2019 (Scopus) identifier

  • 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.