Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions

This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities the properties of discrete fractional calculus serve as fundamental foundation our approach. To help establish main results, an analogous representation equation, called a Volterra-type summation is constructed. Two numerical examples are provided demonstrate validity theoretical findings; no earlier publications been able comment on their solutions’ behavior.