Two-point nonlocal nonlinear fractional boundary value problem with Caputo derivative: Analysis and numerical solution

Abstract This work presents the existential and unique results for solution to a kind of high-order fractional nonlinear differential equations involving Caputo derivative. The boundary condition is integral type, which entangles both starting ending points domain. First, exact extracted in terms Green’s function linear equation, then Banach contraction mapping theorem applied prove main result case general source term. Then, our demonstrated by an illustrative example, shows its legitimacy applicability. Furthermore, numerical-based semi-analytical technique has been presented approximate desired order precision.