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

Year, pages: 2021, 101 - 118

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)Δ^μ u(\ell)]^η] +φ(\ell)f[G(\ell)]=0, \ell\in N_\ell0+1-μ, where \ell₀ ≥ 0,   G(\ell) = ∑\limits_j=\ell0^\ell-1+μ (\ell-j-1)^(-μ)u(j) \end{gather*} and $Δ^μ$ 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.

Chatzarakis, G., Selvam, G., Janagaraj, R., Miliaras, G. 2021. Oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivatives. In Tatra Mountains Mathematical Publications, vol. 79, no.2, pp. 101-118. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0022

Chatzarakis, G., Selvam, G., Janagaraj, R., Miliaras, G. (2021). Oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivatives. Tatra Mountains Mathematical Publications, 79(2), 101-118. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0022

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/