Properties of Green’s function and the existence of different types of solutions for nonlinear fractional BVP with a parameter in integral boundary conditions

Abstract

Abstract This paper is concerned with the impact of the parameter on the existence of different types of solutions for a class of nonlinear fractional integral boundary value problems with a parameter that causes the sign of Green’s function associated with the BVP to change. By using the Guo–Krasnoselskii fixed point theorem, the Leray–Schauder nonlinear alternative, and the analytic technique, we give the range of the parameter for the existence of strong positive solutions, strong negative solutions, negative solutions, and sign-changing solutions for the boundary value problem. Some examples are given to illustrate our main results.

Keywords

• Integral boundary value problem
• Caputo fractional order derivative
• Parameter
• Sign-changing solution
• Cone
• Fixed point