WELL-POSEDNESS FOR MULTIPOINT BVPS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH RIESZ–CAPUTO DERIVATIVE

We propose a class of nonlinear multipoint boundary value problems (BVPs) in the context of fractional differential equations involving the Riesz–Caputo derivative. The nonlinearity term f involves the left Caputo derivative. Under certain conditions, we prove the existence and uniqueness of a solution. Though we apply the standard tools of fixed-point theory to develop the existence and uniqueness criteria for the solutions of the given problem, the results obtained are new in the given scenario. Examples are given to illustrate our main results.