We study two types of bright solitons in zero and non-zero detuning spin-orbit-coupled
Bose-Einstein condensates in fractional effect by variational and imaginary-time evolution
method. The results show that the variation of spin-orbit coupling with fractional kinetic
energy operator affects the existence and form of solitons. In particular, we found that
spin-orbit coupling
strength $\gamma=1.0$ could be a transition point. In other words, for $\gamma < 1.0$ and
$\gamma \geq 1.0$, the soliton states and pseudo-spin polarization in non-zero detuning
show opposite changes. In addition, moving bright solitons with zero and non-zero detuning
are studied.

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