Abstract
We study the fractional dissipative solitons with nonlinear loss and linear gain supported by a special class of PT-symmetric potential in focused nonlinear Kerr medium. The effective width, existence and stability of fractional solitons are discussed. In such a potential, the stability of solitons changes at lower energy. Once the stability of symmetric solitons is destroyed, asymmetric solitons and symmetric solitons coexist. With the increase of linear gain coefficient, the effective width decreases first and then increases. With the increase of Lévy index, the amplitude of solitons decreases. In addition, the change of nonlinear loss coefficient has almost no effect on the soliton contour.
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