Natural Transform along with HPM Technique for Solving Fractional ADE

The authors of this paper solve the fractional space-time advection-dispersion equation (ADE). In process, solute movement being nonlocal in nature and velocity fluid flow nonuniform, it leads to form a heterogeneous system which approaches model same by means ADE generalizes classical ADE, where time derivative is substituted through Caputo derivative. For study such models, various numerical techniques are used researchers but nonlocality causes high computational expenses complex calculations so challenge use an efficient method involves less computation accuracy solving models numerically. Here, order get FADE solved convergent infinite series, novel NHPM (natural homotopy perturbation method) applied couples Natural transform along with method. peturbation has been mathematical physics many initial value problems expressed PDEs. Also, HPM advantage over other methods that does not require any discretization domains, independent physical parameters, only uses embedding parameter p ∈ 0 , 1 . combined rapidly series solutions computation. efficacy shown working out some examples for time-fractional conditions using NHPM. Mittag-Leffler function problem, impact changing id="M2"> α on concentration all cases.