Existence And Uniqueness Of Solutions For Fractional Q-difference Equation With P-laplacian Operator

In recent years,q-difference theory has developed rapidly as an important branch of discrete mathematics.It plays an important role in the fields of math-ematical physics models,dynamic systems,quantum models etc.Due to its wide applicability,the existence and uniqueness of the solutions of the boundary val-ue problem of fractional order q-difference equations has attracted the attention of domestic and foreign scholars.In this paper,we mainly study the existence and uniqueness of positive solutions for boundary value problems of fractional q-difference equations with p-Laplacian operator.In the second chapter,we consider the existence of positive solutions for a class of fractional q-difference system boundary value problem.The fractional q-difference system boundary value problem is converted into equivalent integral equation to calculate the system boundary value problem of the Green function and analyses the nature of the Green function.By using the monotone iterative method,we obtain the existence result of the solutions of fractional q-difference system boundary value problem.In the third chapter,we consider the existence and uniqueness of the solution of the boundary value problem for singular nonlinear fractional q-difference equations.The existence and uniqueness of the solution of the boundary value problem are proved by the fixed point theorem.