Pseudo Asymptotically Periodic Solutions For A Class Of Fractional Differential Equations With Delay

In the past decades, the theory of fractional differential equations has become an important area of investigation because of its wide applicability in many branches of viscoelasticity, electrochemistry, control and electromagnetic. The study of the existence of periodic solutions is one of the most important topics in the qualitative theory of differential equations, which properties of the solutions have been studied in several contexts, for example, invariant manifolds theory, convergence theory, discrete maximal regularity, asymptotic behavior, exponential dichotomy, robustness, stability, and periodicity.In recent years, we notice that some investigations have been done on the existence and uniqueness of solutions for fractional differential equations with delay, including:periodic solutions, asymptotic periodic solution and almost periodic solution,S-asymptotic w-periodic solution, and in this thesis we will explore the existence and uniqueness of pseudo S-asymptotically w-periodic solutions for a class of abstract neutral fractional differential equations with finite delay.In this thesis, we study the existence and uniqueness of pseudo S-asymptotically w-periodic solutions for a class of abstract neutral fractional differential equations with finite delay, which is based on the pseudo S-asymptotically w-periodic solutions for a class of fractional differential equations. Using the fixed point theorem and compression mapping principle, firstly, on the promise of existing mild solution of equation, we verify the Nemytskii mapping which meets the conditions by the sufficient conditions of pseudo S-asymptotically w-periodic solutions. Then, we verify the existence and uniqueness of pseudo S-asymptotically w-periodic solutions for a class of abstract neutral functional differential equations with finite delay separately from three different cases: the bounded Lipschitz continuous, bounded locally Lipschitz continuous and unbounded Lipschitz continuous. And in the last part, using the front conclusion, we give three concrete fractional partial differential equations with delay and analyze the sufficient conditions of pseudo S-asymptotically w-periodic solutions for three equations.