On the Extremal Solution for a Nonlinear Boundary Value Problems of Fractional p-Laplacian Dierential Equation

Abstract

This paper is concerned with the existence and uniqueness of
extremal solution for a nonlinear boundary value problems of
fractional $p$-Laplacian differential equation involving
Riemman-Liouville derivative. By applying the monotone iterative
technique and the method of lower and upper solutions, we obtain
sufficient conditions for existence and uniqueness of extremal
solution and construct the sequence of iterations to approximate it.
The paper extends the applications of lower and upper solutions
method.