FRACTIONAL BENJAMIN–BONA–MAHONY–BURGES EQUATIONS ON BOUNDED DOMAINS

We study an initial-boundary value problem for the nonlinear fractional Benjamin–Bona–Mahony–Burges equation on the interval [0,1]. Using a Green’s function approach and the integration by parts, we obtain an integral representation of solutions for the associated linear problem, then using the existence and uniqueness of fixed points of contractions in complete metric spaces, we prove the existence and uniqueness of solutions.