Multiplicative fractional integral inequalities for multiplicative $s$-convex functions: A multi-parameter approach

Abstract

Within the multiplicative Riemann--Liouville (RL) fractional framework, we develop multi-parameter inequalities for multiplicatively differentiable $s$-convex positive functions. Using a multi-parameter multiplicative fractional integral identity, we establish several inequalities under the conditions: (i) $\Psi^{*}$ exhibits multiplicative $s$-convexity, and (ii) $(\ln \Psi^{*})^q$ maintains $s$-convexity($q>1$). Numerical examples and graphical visualizations verify the proposed inequalities.