Qualitative dynamical study of hybrid system of Pantograph equations with nonlinear p-Laplacian operator in Banach’s space

This study provides a comprehensive exploration of the qualitative analysis of a hybrid system of pantograph equations with fractional order and a p-Laplacian operator. The existence of the solution of the system is explicitly established within the context of Riemann–Liouville's fractional order operator, employing the Arzelà–Ascoli theorem for validation. The establishment of uniqueness criteria is accomplished by the utilization of the Banach contractive technique. In addition, the examination of solution stability is conducted using the Hyers–Ulam (HU) stability technique. In order to enhance the credibility of our main conclusions, we have included a representative and illustrative example in the concluding section of the study. This work serve to offer a thorough and applicable comprehension of the mathematical framework that has been proposed.