Oscillatory behavior of solutions of certain fractional difference equations

ADIGÜZEL H.

Advances in Difference Equations, vol.2018, no.1, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2018 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1186/s13662-018-1905-3
  • Journal Name: Advances in Difference Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Fractional difference equations, Fractional difference operator, Hardy inequalities, Oscillation, Oscillation criteria, Riccati technique, Riemann–Liouville
  • Istanbul Gelisim University Affiliated: Yes

Abstract

© 2018, The Author(s).In this paper, we consider the oscillation behavior of solutions of the following fractional difference equation: Δ (c(t) Δ (a(t) Δ (r(t) Δ αx(t)) + q(t) G(t) = 0 , where t∈Nt0+1−α, G(t)=∑s=t0t−1+α(t−s−1)−αx(s), and Δ α denotes a Riemann–Liouville fractional difference operator of order 0 < α≤ 1. By using the generalized Riccati transformation technique, we obtain some oscillation criteria. Finally we give an example.