Multiple positive solutions of integral BVPs for high-order nonlinear fractional differential equations with impulses and distributed delays

Abstract

In this article, we study the existence of multiple solutions of the integral boundary value problems for high-order nonlinear fractional differential equations with impulses and distributed delays. Some sufficient criteria will be established by the fixed point index theorem in cones. As application, one example is given to demonstrate the validity of our main results.

Keywords:

• distributed delays
• multiple positive solutions
• integral boundary value problems
• impulsive fractional differential equations
• fixed point index theorem

MCS/CCS/AMS Classification/CR Category numbers:

• 34B10
• 34B15
• 34B37

Acknowledgements

The author would like to thank the anonymous referees for their useful and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the National Natural Sciences Foundation of Peoples Republic of China [grant number 11161025]; Yunnan Province natural scientific research fund project [grant number 2011FZ058].