On Fractional Sturm–Liouville Problems with Complex Coefficients

We investigate the existence and uniqueness of solutions for two-point boundary value problems involving left and right Caputo fractional derivatives with possibly complex-valued coefficients on a finite real interval. Under suitable assumptions on the fractional order and the coefficients, we establish the existence and uniqueness of continuous weak solutions. In addition, under further L2-type assumptions on the coefficients, we prove the existence of weak solutions in the Hilbert space L2(a,b). The analysis is based on an equivalent fractional integral formulation and the Banach–Caccioppoli fixed-point theorem.