本项目旨在建立时标上分数阶Sobolev空间作为工作空间，应用临界点理论研究时标上分数阶Hamiltonian系统的如下三个问题：.(1)研究时标上分数阶Hamiltonian系统解的存在性、多重性以及同宿解、异宿解的存在性问题；.(2)研究时标上分数阶时滞Hamiltonian系统概周期解的存在性和多重性；.(3)分析时标上奇异分数阶Hamiltonian系统中脉冲扰动的作用，即研究时标上具脉冲项的奇异分数阶Hamiltonian系统概周期解的存在性和多重性，探索时标上奇异分数阶Hamiltonian系统具有脉冲生成的概周期解的条件，考察脉冲扰动对时标上奇异分数阶Hamiltonian系统次调和解的影响。本项目的研究将不仅发展和完善时标上分数阶Hamiltonian系统的理论，还将进一步扩展变分方法和临界点理论的应用范围，具有重要的理论意义和广泛的应用前景。

This project aims to define the fractional order Sobolev's spaces on time scales as the work spaces for studying fractional order Hamiltonian systems on time scales by critical point theory. we will study the project as follows:.(1)We will study the existence and multiplicity of solutions, homoclinic solutions and heteroclinic solutions of fractional order Hamiltonian systems on time scales;.(2)We will study the existence and multiplicity of almost periodic solutions for fractional order Hamiltonian systems with delay on time scales;.(3)We will analysis the impact of impulsive perturbation on the solutions of singular fractional order Hamiltonian systems on time scales, Firstly, the existence and multiplicity of almost periodic solutions for singular fractional order Hamiltonian systems with impulsive effects on time scales are studed. Secondly, some sufficient conditions will be established for almost periodic solutions of singular fractional order Hamiltonian systems on time scales generated by impulses. Thirdly, subharmonic solutions of singular fractional order Hamiltonian systems with impulsive effects on time scales will be discussed. .The research of this project will not only develop the theory of fractional order Hamiltonian systems on time scales, but also will further extend the own range of applications of critical point theory. Therefore, this project has important theoretical and practical values.