  In this paper one-weight inequalities with general weights for
Riemann-Liouville transform and $ n-$ dimensional fractional integral operator
in variable exponent Lebesgue spaces defined on $\mathbb{R}^{n}$ are
investigated. In particular, we derive necessary and sufficient conditions
governing one-weight inequalities for these operators on the cone of
non-negative decreasing functions in $L^{p(x)}$ spaces.
