A Certain Numerical Algorithm for Solving a Fractional Partial Model with a Neumann Constraint in a Hilbert Space

This research examines a fractional partial advection–dispersion model, incorporating both mobile and immobile components, employing the Hilbert reproducing algorithm under an appropriate Neumann constraint condition. To effectively formulate the model while adhering to the specified constraints, two suitable Hilbert spaces are constructed, with the time-fractional Caputo derivative being utilized in the model’s formulation. Alongside the convergence analysis, a derived approximate solution formula is presented, and a systematic computational algorithm is developed to effectively implement the solution methodology. Numerical applications related to the proposed model are presented, complemented by tables and graphical illustrations. In conclusion, significant results are analyzed, and directions for future research are outlined.