A reliable analytical approach for a fractional model of advection-dispersion equation - Singh, Jagdev; Secer, Aydin; Swroop, Ram; Kumar, Devendra (WALTER DE GRUYTER GMBH, 2019)
Empirical investigations of solute fate and carrying in streams and rivers often contain inventive liberate of solutes at an upstream perimeter for a finite interval of time. An analysis of various worth references on surfacewater-grade mathematical formulation reveals that the logical solution to the continual-parameter advection- dispersion problem for this type of boundary state has been generally missed. In this work, we study the q-fractional homotopy analysis transform method (q-FHATM) to find the analytical and approximate solutions of space-time arbitrary order advection-dispersion equations with nonlocal effects. The diagrammatical representation is done by using Maple package, which enhance the discretion and stability of family of q-FHATM series solutions of fractional advection-dispersion equations. The efficiency of the applied technique is demonstrated by using three numerical examples of space- and time-fractional advection-dispersion equations.
Keywords: Fractional advection-dispersion problem; Laplace transform method; q-fractional homotopy analysis transform technique; Mittage-Leffler function; Engineering; Mathematics