Abstract
Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Delta*(beta)[k](t) = w(t+beta,k(t+beta),k(lambda(t+beta)), with condition k(0) = p[k] for t is an element of N1-beta, 0 < beta <= 1, lambda is an element of (0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii's and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.