Periodic boundary value problems for impulsive conformable fractional integro-differential equations

Boundary value problems

Phollakrit Thiramanus¹  Jessada Tariboon²  Suphawat Asawasamrit³  Sotiris K Ntouyas⁴ 

[1] Department of Mathematics, University of Ioannina, Ioannina, Greece;Nonlinear Analysis and Applied Mathematics (NAAM) - Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

关键词: periodic boundary value problem;    conformable fractional derivative;    impulsive differential equation;    monotone iterative technique;    lower and upper solutions;    26A33;    34A08;    34A37;   

DOI  :  10.1186/s13661-016-0629-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is concerned with the existence of solutions for periodic boundary value problems for impulsive fractional integro-differential equations using a recent novel concept of conformable fractional derivative. We give a new definition of exponential notations and impulsive integrals for constructing the Green function and a comparison result of the linear problems with impulses. By applying the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, some new sufficient conditions for the existence of solutions are established. The obtained results are well illustrated by an example.

【 授权许可】

CC BY