To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition

In this paper, we prove the existence and uniqueness of the solutions for a non-integer high order boundary value problem which is subject to the Caputo fractional derivative. The boundary condition is a non-local type. Analytically, we introduce the fractional Green’s function. The main principle applied to simulate our results is the Banach contraction fixed point theorem. We deduce this paper by presenting some illustrative examples. Furthermore, it is presented a numerical based semi-analytical technique to approximate the unique solution to the desired order of precision.

Keywords:

High order fractional differential equation , Caputo fractional derivative , Boundary value problem , Existence and uniqueness , fixed point theorem