On the oscillation of certain discrete fractional difference equations with delay

Abstract

In this thesis we employ the properties of left nabla Caputo difference operator and the discrete nabla Laplace transform on , to investigate the oscillatory behavior of solutions for two classes of fractional delay difference equations. The first one is with one positive coefficient and the second one is with two positive coefficients. Besides we give generalization for the two classes and study their oscillatory patterns. We show that the solutions act oscillatory if certain characteristic equations have not real roots. By applying the operator, we prove the oscillatory for right nabla Caputo difference. Finally, two classical real life mathematical models on delay differential equations are applied to present our new results.