Abstract
In this article, we establish new Hermite-Hadamard-type inequalities via Riemann-Liouville integrals of a function psi taking its value in a fractal subset of R and possessing an appropriate generalized s-convexity property. It is shown that these fractal inequalities give rise to a generalized s-convexity property of psi. We also prove certain inequalities involving Riemann-Liouville integrals of a function psi provided that the absolute value of the first or second order derivative of psi possesses an appropriate fractal s-convexity property.