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

Alsadi, Wadhah Ahmed; Hussein, Mokhtar; Abdullah, Tariq Q. S.

doi:10.22034/cmde.2021.32807.1580

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.

10.22034/cmde.2021.32807.1580

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

20.1001.1.23453982.2021.9.4.8.0

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