New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators

Abstract

In this work, a new strategy to derive inequalities by employing newly proposed fractional operators, known as a Hilfer generalized proportional fractional integral operator ($\widehat{\mathcal{GPFIO}}$). The presented work establishes a relationship between weighted extended \v{C}eby\v{s}ev version and P\'{o}lya-Szeg\"{o} type inequalities, which can be directly used in fractional differential equations and statistical theory. In addition, the proposed technique is also compared with the existing results. This work is important and timely for evaluating fractional operators and predicting the production of numerous real-world problems in varying nature.

Keywords

• integral inequality
• λ-generalized proportional fractional integral
• čebyšev inequality
• pólya-szegö inequality