SOLVABILITY OF A FRACTIONAL BOUNDARY VALUE PROBLEM WITH <i>P</i>-LAPLACIAN OPERATOR ON AN INFINITE INTERVAL

Abstract

In this paper, we extend the third order $ p $-Laplacian boundary value problem researched by S. Iyase and O. Imaga in [11] to the fractional differential equation. Firstly, we construct a mild Banach space and establish an appropriate compactness criterion. Then applying the Schauder's fixed point theorem, we obtain a sufficient condition for existence of at least one solution to the fractional differential equation with $ p $-Laplacian operator on an infinite interval. As an application, an example is given to illustrate our main result.