Oscillation Theorems for Certain Forced Nonlinear Discrete Fractional Order Equations - Chatzarakis, George E.; Selvam, A. George Maria; Janagaraj, R.; Douka, Maria (Communications in Mathematics and Applications, 2019)
The main objective of this work is to obtain some new sufficient conditions that are essential for the oscillation of the solutions of forced nonlinear discrete fractional equations of the form \begin{align*} \Delta\left[\Delta^\mu(u(j))\right]+\eta(j)\Phi(u(j))=\psi(j), \ \ j\in N_0 \end{align*} where \(\Delta^{\mu-1}u(0)=u_0\); \(\Delta u(j)=u(j+1)-u(j)\) and \(\Delta^\mu\) is defined as the difference operator of the Riemann-Liouville (R-L) derivative of order \(\mu\in(0,1]\) and \(N_0=\{0,1,2,\cdots\}\). Numerical examples are presented to show the validity of the theoretical results.