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Let $M_{\beta }$ be the fractional maximal function. The commutator generated by $M_{\beta }$ and a suitable function $b$ is defined by $[M_{\beta },b]f=M_{\beta }\left(bf\right)-b{M}_{\beta }\left(f\right)$. Denote by $𝒫\left({ℝ}^n\right)$ the set of all measurable functions $p(·):{ℝ}^n\to [1,\infty )$ such that $$1<p_{-}:=\underset{x\in {ℝ}^n}{\mathrm{ess}\inf }p\left(x\right)\text{and}{p}_{+}:=\underset{x\in {ℝ}^n}{\mathrm{ess}\sup }p\left(x\right)<\infty ,$$ and by $ℬ\left({ℝ}^n\right)$ the set of all $p(·)\in 𝒫\left({ℝ}^n\right)$ such that the Hardy-Littlewood maximal function $M$ is bounded on $L^{p(·)}\left({ℝ}^n\right)$. In this paper, the authors give some characterizations of $b$ for which $[M_{\beta },b]$ is bounded from $L^{p(·)}\left({ℝ}^n\right)$ into $L^{q(·)}\left({ℝ}^n\right)$, when $p(·)\in 𝒫\left({ℝ}^n\right)$, $0<\beta <n/p_{+}$ and $1/q(·)=1/p(·)-\beta /n$ with $q(·)(n-\beta )/n\in ℬ\left({ℝ}^n\right)$.