Numerical approximation method for hybrid non-linear Caputo fractional differential equations with boundary value conditions

We address the problem of existence, uniqueness and approximation of the solution of a large class of fractional integral differential equations with boundary conditions. Based on fixed point techniques with Boyd-Wong type conditions, the existence and uniqueness of the solution is investigated. This, together with the use of certain types of biorthogonal systems, allows us to propose a method to approximate the solution which is tested with several examples.