On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application

Abstract

Abstract Post-quantum integral inequalities involving the Riemann–Liouville fractional integral have a significant role in understanding and modeling systems with nonlocal interactions; anomalous diffusion and memory effects make them indispensable for addressing modern challenges in applied mathematics and physics. In this paper, the authors introduced a right fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type, including the q-shifting operator, in parallel to the left fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type introduced by Neang et al. This is done to investigate the post-quantum multiparameter fundamental identity of continuous functions on finite intervals and to derive some new and existing estimates of various inequalities, such as Bullen type, Simpson type, midpoint type, trapezoid type, etc. In order to verify the accuracy of the findings, graphical and numerical analysis and an application to special means are provided.

Keywords

• q-calculus
• q-shifting operator
• ( p , q ) $(p,q)$ -calculus
• Fractional ( p , q ) $(p,q)$ -integral
• Fractional ( p , q ) $(p,q)$ -integral inequality