In this research, we use a novel version of the Extended Direct Algebraic Method (EDAM) namely generalized EDAM (gEDAM) to investigate periodic soliton solutions for nonlinear systems of fractional Schrödinger equations (FSEs) with conformable fractional derivatives. The FSEs, which is the fractional abstraction of the Schrödinger equation, grasp notable relevance in quantum mechanics. The proposed gEDAM technique entails creating nonlinear ordinary differential equations via a fractional complex transformation, which are then solved to acquire soliton solutions. Several 3D and contour graphs of the soliton solutions reveal periodicity in the wave profiles that offer crucial perspectives into the behavior of the system. The work sheds light on the dynamics of FSEs by displaying numerous families of periodic soliton solutions and their intricate relationships. These results hold significance not only for comprehending the dynamics of FSEs but also for nonlinear fractional partial differential equation applications.

在这项研究中，我们使用扩展直接代数方法 (EDAM) 的新版本，即广义 EDAM (gEDAM) 来研究具有一致分数阶导数的分数薛定谔方程 (FSE) 非线性系统的周期孤子解。 FSE 是薛定谔方程的分数抽象，它在量子力学中具有显着的相关性。所提出的 gEDAM 技术需要通过分数复数变换创建非线性常微分方程，然后求解该方程以获得孤子解。孤子解的几个 3D 和等值线图揭示了波剖面的周期性，为系统行为提供了重要的视角。这项工作通过展示众多周期性孤子解及其复杂关系，揭示了 FSE 的动态。这些结果不仅对于理解 FSE 的动力学具有重要意义，而且对于非线性分数偏微分方程应用也具有重要意义。