Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term

Rok, strany: 2020, 1165 - 1182

The aim in this work is to investigate oscillation criteria for a class of nonlinear discrete fractional order equations with damping term of the form

$$ Δ[a(t)[Δ(r(t)g(Δ^α x(t)))]^β]+p(t)[Δ(r(t)g(Δ^α x(t)))]^β+F(t,G(t))=0, t\in N_t0. $$

In the above equation $α$ $(0<α≤ 1)$ is the fractional order, $G(t)=∑\limits_s=t0^t-1+α(t-s-1)^(-α)x(s)$ and $Δ^α$ is the difference operator of the Riemann-Liouville (R-L) derivative of order $α$. We establish some new sufficient conditions for the oscillation of fractional order difference equations with damping term based on a Riccati transformation technique and some inequalities. We provide numerical examples to illustrate the validity of the theoretical results.

ISO 690:

Chatzarakis, G., Selvam, G., Janagaraj, R., Miliaras, G. 2020. Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term. In Mathematica Slovaca, vol. 70, no.5, pp. 1165-1182. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0422

APA:

Chatzarakis, G., Selvam, G., Janagaraj, R., Miliaras, G. (2020). Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term. Mathematica Slovaca, 70(5), 1165-1182. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0422

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava