ON SOME RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL INEQUALITIES

Abstract

This paper presents some new extensions of the Riemann-Liouville and Katugampola frac- tional integral inequalities. Tempered fractional operators are incorporated in this study to generalize various results available recently. By replacing classical convexity with the broader concept of h-convexity, more flexible conditions are obtained. Using these as- sumptions, we determine new upper bounds for the so-called tempered fractional integrals. The boundedness of Katugampola fractional integrals is also investigated in detail. These results provide sharper estimates compared to the classical fractional inequalities. The gen- erality of the derived inequalities is further enhanced through exponential tempering. Many existing results are recovered as special cases of our main findings. The obtained inequali- ties unite and further extend several known fractional integral results. The results obtained are useful in mathematical analysis and various applied models. The thesis gives broader and stronger tools to deal with fractional inequalities. It opens new directions for further research in generalized fractional operators.