分数维在自然界和科学技术中广泛存在，并且越来越多的被用来描述各种系统中的复杂或反常问题。近几年，分数维系统中光束的传输特性也备受关注。另一方面，宇称-时间(PT)和Partially-PT对称系统也因为具有许多新颖独特的性质而成为光学领域的前沿。本项目基于非线性分数薛定谔方程描述的系统，拟从理论方面揭示分数阶衍射下PT/Partially-PT对称势场调控的非线性系统中空间孤子的特性，发现其中的新现象，探索孤子调控的新机制。拟开展以下几方面的工作：（1）研究分数PT带隙孤子中分数阶衍射效应和各种不同的非线性效应的平衡机制（2）研究双组分矢量分数PT孤子的存在性，稳定性（3）比较分数阶衍射下的涡旋孤子在Partially-PT对称方位角势场和PT对称势场中的差异（4）变分法分析分数阶PT孤子的动力学行为。本项目的研究不仅能扩展人们对孤子的认知，也可以为分数维非线性系统的发展提供参考。

Fractional dimensions exist extensively in nature, science and technology, and it is now increasingly used to describe the complex or anomalous problems in various systems. In recent years, optical beam propagation in these fractional systems has received much attention. On the other hand, the Parity-time (PT) and Partially-PT symmetric systems have already become the frontier research fields of optics because of their many new unique properties. The project is based on the systems described by nonlinear fractional Schrödinger equations, trying to reveal theoretically the features of spatial solitons supported by PT/Partially-PT symmetric potentials with fractional-order diffraction and nonlinear effects, find some new phenomenon, and explore new mechanisms for regulating soliton. The research work will focus on the following aspects: (1) learn the balance mechanism of fractional PT gap solitons between the fractional-order diffraction effect and kinds of different nonlinear effects (2) study the existence and stability of two-component vector fractional PT solitons (3) compare the differences of fractional vortex solitons between Partially-PT symmetric azimuthal potentials and PT symmetric potentials (4) analyses the dynamical behavior of fractional PT optical solitons by the variational approach. The research not only expand people's knowledge on solitons, but also provide reference for the development of fractional nonlinear systems.