Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem

Document Type : Research Paper

Authors

1 School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China

2 School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China.

3 School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China.

Abstract

In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with Φp-Laplacian operator. Our problem is based on Caputo fractional derivative of orders σ, ϵ, where k − 1 < σ, ϵ ≤ k, and k ≥ 3. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result.

Keywords