A Study of Generalized Hybrid Discrete Pantograph Equation via Hilfer Fractional Operator

Pantograph, a device in which an electric current is collected from overhead contact wires, introduced to increase the speed of trains or trams. The work aims study stability properties nonlinear fractional order generalized pantograph equation with discrete time, using Hilfer operator. Hybrid fixed point theorem considered existence solutions, and uniqueness solution proved Banach contraction theorem. Stability results sense Ulam Hyers, its form for initial value problem are established we depict numerical simulations demonstrate impact on stability.