Research On The Existence Of Solutions For Boundary Value Problem Of Nonlinear Fractional Differential Equations With P-Laplacian Operator

The appearance of fractional differential equations is the results of the continuous improvement and expansion of the classical and immemorial differential equations. Comparing with the integer order differential equations, the solutions of fractional differential equations are more precised on the calculational results. Hence,the fractional differential equations have been widely applied in mathematical biology, electronic communications, the viscoelastic disciplines mechanics, atmospheric dynamics, and so on. In many practical applications of physics, the fractional differential equations with p-Laplacian operators, can solve some complex physical phenomena better. So the fractional differential equations not only make the obtained solution more accurately, but also benifit to describe some complex physical phenomena process. And the research methods has become a hot theory in physics practical problems. This paper focuses on the existence of solution of boundary value problems.And it obtain existence conditions of the solution by some appropriate method.This article consists of three parts.The first part is an introduction, it mainly introduces the historical background and the present research statuation of the problem. This part also introduces the basic definition and fundamental theorem which used in the paper.The second part, it studies boundary value problems for a class of coupled system of fractional differential equations with a p-Laplacian operatora, which making use of relevant properties of the Green's function and proving the conditions of existence by the fixed point theorem to discuss the existence of solution. Then, it can obtain a suitable solution.The third part, it studies boundary value problem for a class of nonlinear fractional differential equation with p-Laplacian operator at resonance. It uses uses the relevant properties of the Green's function, Schauder fixed point theorem and mean value theorem to obtain the sufficient conditions for the results of the existence of solution.