Study On Fractional Differential Equations And Non Stationary Generalized Variational Inequalities

Fractional order differential equation and generalized variational inequality problem are two new type problems and have very important research significance,this article mainly solves two problems,the first question is fractional order differential equations and inclusions with nonlocal Erdelyi-Kober integral boundary value conditions,among them,according to the principle of compression mapping and fixed point theorems solve the problem of the existence and uniqueness of solution,using nonlinear choose of compression mapping discuss differential inclusion problems;The second problem is that using penalty function method solves the non-stationary generalized variational inequalities.Firstly,we introduce what is the generalized variational inequalities and the penalty function,then the penalty function method is applied to non-stationary generalized variational inequality problem.The first chapter,we mainly tell the research background of the fractional order differential equation and the generalized variational inequality,and their research status at home and abroad,and the full text frame.The second chapter,we introduce relevant knowledge to fractional order differential equations and inclusions problem with nonlocal Erdelyi-Kober integral boundary value conditions and generalized variational inequality problems,including the definition,nature and lemma.The third chapter,our mainly study is what under conditions,fractional order differential equations and inclusions problem's with nonlocal Erdelyi-Kober integral boundary value conditions the existence and uniqueness of solution.The fourth chapter,we focus on how to use the penalty function method solve the problem of generalized variational inequality.Finally,the fifth chapter,we summarize the current work,and discuss the future of work.