Stable and oscillating solitons of $$\pmb {\mathcal {PT}}$$-symmetric couplers with gain and loss in fractional dimension

Families of coupled solitons $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension settings without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, propagation dynamics the obtained investigated. By comparing results CIM, we find that area model CIM is much broader than one CIM. Remarkably, oscillating can also exist same coefficients self- modulations. In addition, period these be controlled by linear coupling coefficient.