Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

Longfei Lin,Yansheng Liu,Daliang Zhao

doi:10.3390/math9040300

Abstract

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results.

Highlights

IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
This paper aims to establish the sufficient conditions for the existence and stability results of solutions to a class of coupled systems of implicit-type fractional differential equations (IFDEs) involving Caputo fractional derivatives under the integral-type boundary conditions
It is well known that the subject of fractional differential equations (FDEs) has gained considerable popularity and importance due to its wide range of applications in describing the real word problems

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. This paper aims to establish the sufficient conditions for the existence and stability results of solutions to a class of coupled systems of implicit-type fractional differential equations (IFDEs) involving Caputo fractional derivatives under the integral-type boundary conditions Dαx(t) =. It is well known that the subject of fractional differential equations (FDEs) has gained considerable popularity and importance due to its wide range of applications in describing the real word problems. FDEs are powerful tools to model the many phenomena of different fields of scientific disciplines and engineering. The study of FDEs is found to be of great value and interest in view of the occurrence of such systems in a variety of problems of applied nature.

Objectives

Results

Conclusion