In this work, we introduce and theoretically analyze a relatively simple numerical algorithm
to solve a double-fractional condensate model. The mathematical system is a generalization of
the famous Gross–Pitaevskii equation, which is a model consisting of two nonlinear complexvalued diffusive differential equations. The continuous model studied in this manuscript is a
multidimensional system that includes Riesz-type spatial fractional derivatives. We prove here the
relevant features of the numerical algorithm, and illustrative simulations will be shown to verify the
quadratic order of convergence in both the space and time variables.
