Existence Of Positive Solutions For Delta-nabla Fractional Boundary Value Problems With P-laplacian

In recent years,with the development of mathematics,the mathematical model of fractional order difference equation has been found by people,and making people set up more and more high request to the approximate solutions of fractional order difference equations.What is more,with the development of fractional order differential equation,fractional order difference equation has no longer limited to pure theoretical research,and applied to practical problems,such as biology,physics and so on.And the fractional order differential equation has became to one of the popular field concerned by the scholars.On the other hand the further research of fractional order differential equation could help us to improve the function equation of the theory and application of basic work,and provide a lot of support for the research of other functional equation.This paper mainly studies the following delta-nabla boundary value problem for the fractional difference equation with p-Laplacian(?)(?)(?)(?)By using the mathod of transformation,we can get a transformed fractional boundary value problems,as follow(?)(?)(?)And we prove the existence of positive solutions for the transformed problems with using the method of upper and lower solution and Schauder fixed point theorem.Consequently,we can also prove the existence of positive solutions for the first fractional boundary value problems.Next,we can set up the monotone iterative technique and obtain the approximate solutions of the transformation problems,the results can be also available to get the original equations' approximate algorithm.