On the Stability Properties of Retarded Volterra Integro-Fractional Differential Equations with Caputo Derivative

Hristova S., Tunç C.

7th International Conference on New Trends in the Applications of Differential Equations in Sciences (NTADES), St Constantin and Helena, Bulgaristan, 1 - 04 Eylül 2020, cilt.2321 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2321
  • Doi Numarası: 10.1063/5.0040076
  • Basıldığı Şehir: St Constantin and Helena
  • Basıldığı Ülke: Bulgaristan
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, the direct Lyapunov method is extended to fractional case of Volterra integro-Caputo fractional differential equations with delays. Two types of homogeneous scalar Voterra integro-Caputo fractional differential equations with delays are studied. Three types of fractional derivatives of Lyapunov functions known in the literature are given. Uniform stability of trivial solution of that retarded IFrDEs is investigated using the Razumikhin method and different types of fractional derivatives of Lyapunov functions. Examples to show the application of the theorems are provided.