On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative

The pantograph equation is a special type of delay differential equation with applications in quantum mechanics and electrodynamics. A generalized hybrid pantograph equation of fractional order involving deformable derivative is considered in this work to carry out the stability analysis. The existence of solutions is established by employing the measure of noncompactness and Darbo’s fixed point theorem while the contraction mapping principle is used for proving the uniqueness of the solution.  The link between the right-hand term of the given equation and the order of the deformable derivative is established. The paper presents the results on Ulam-Hyers stability and the generalized Ulam-Hyers stability of the proposed equation. Numerical simulations are provided to demonstrate the performed theoretical analysis.