EXISTENCE OF NONTRIVIAL SOLUTIONS FOR AN INTEGRAL BOUNDARY VALUE PROBLEM INVOLVING THE CAPUTO-FABRIZIO-TYPE FRACTIONAL DERIVATIVE

In this work we study the existence of nontrivial solutions for a Caputo-Fabrizio-type fractional integral boundary value problem. We first construct a new linear operator, which can include the integral boundary condition, and then under some conditions involving the spectral radius of the linear operator, we use topological degree methods to obtain some existence theorems for our considered problem.