Some post quantum Milne type inequalities with simulation

Post quantum Milne-type inequalities involving the Riemann-Liouville fractional integral offer mathematical frameworks for evaluating and bounding quantum states and for addressing modern challenges in applied mathematics and physics. In this paper, a right fractional (p,q)−integral operator of Riemann-Liouville type, including the q-shifting operator, is used to investigate the post-quantum multiparameter fundamental identity of continuous functions on finite intervals and to derive some new and existing estimates of Milne-type inequalities. In order to verify the accuracy of the findings, graphical and numerical analysis and an application to special means are provided.