# Oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivatives

In: Tatra Mountains Mathematical Publications, vol. 79, no. 2
George E. Chatzarakis - George M. Selvam - Rajendran Janagaraj - George N. Miliaras

## Details:

Year, pages: 2021, 101 - 118
Language: eng
Keywords:
oscillation, Riemann-Liouville fractional derivatives, difference equations
Article type: Mathematics
Document type: scientific paper
Based on the generalized Riccati transformation technique and some inequality, we study some oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivative equation \begin{gather*} Δ[γ(\ell) [α(\ell) +β(\ell)Δμ u(\ell)]η] +φ(\ell)f[G(\ell)]=0, \ell\in N\ell0+1-μ, where \ell0 ≥ 0,   G(\ell) = ∑\limitsj=\ell0\ell-1+μ (\ell-j-1)(-μ)u(j) \end{gather*} and $Δμ$ is the Riemann-Liouville (R-L) difference operator of the derivative of order $μ$, $0 ≤ μ ≤ 1$ and $η$ is a quotient of odd positive integers. Illustrative examples are given to show the validity of the theoretical results.