New W−W-weighted concepts for continuous random variables with applications

New concepts on fractional probability theory are introduced and some inequalities for the fractional $w-$weighted expectation and the fractional $w-$weighted variance of continuous random variables are obtained. Other fractional results related to the two orders-fractional $w-$% weighted moment are also established. Some recent results on integral inequality theory can be deduced as some special cases. At the end, some applications on the uniform random variable are given