Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives

Jianfang Qin,Guotao Wang,Lihong Zhang,Bashir Ahmad

doi:10.1186/s13661-019-1254-5

Abstract

By using monotone iterative method, the extremal solutions and the unique solution are obtained for a nonlinear fractional p-Laplacian boundary value problem involving fractional conformable derivatives and nonlocal integral boundary conditions. Comparison theorems related to the proposed study are also proved. The paper concludes with an illustrative example for the main result.

Highlights

1 Introduction Fractional calculus provides powerful tools to deal with complex phenomena occurring in various areas of applied and technical sciences such as control theory, optical and thermal systems, rheology, materials and mechanical systems, robotics, etc
For some recent results on Riemann–Liouville fractional differential equations, we refer the reader to the articles [11–15] and the references cited therein
The literature on fractional differential equations equipped with integral boundary conditions contains a variety of interesting results [27–32]

Summary

Introduction

Fractional calculus provides powerful tools to deal with complex phenomena occurring in various areas of applied and technical sciences such as control theory, optical and thermal systems, rheology, materials and mechanical systems, robotics, etc. We apply monotone iterative method to prove the existence of extremal and uniqueness of solutions for the following nonlinear fractional p-Laplacian problem involving fractional conformable derivatives and nonlocal integral We emphasize that the results obtained for problem (1.1) are new and significantly contribute to the existing literature on p-Laplacian problems with fractional conformable derivatives.

Results

Conclusion