Existence and oscillation results for the Hybrid generalized pantograph Hilfer fractional difference equation

The objective of this study is to analyze the hybrid generalized pantograph Hilfer fractional difference equation's existence, uniqueness and oscillatory behaviour.Our technique, in contrast to previous approaches in the literature, is based on certain newly defined features of discrete fractional calculus and a few mathematical inequalities.The hybrid fixed point theorem has been used to investigate the existence of solutions, and the Banach contraction theorem has been used to show that the solution is unique.Furthermore, a set of adequate requirements is deduced to guarantee oscillation in the solutions of the hybrid generalized pantograph Hilfer fractional difference equation.We provide two numerical simulations at the end of the article to demonstrate the effects of the main results.