A reliable analytical approach for a fractional model of advection-dispersion equation

Singh J., SEÇER A. , Swroop R., Kumar D.

NONLINEAR ENGINEERING - MODELING AND APPLICATION, vol.8, no.1, pp.107-116, 2019 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1515/nleng-2018-0027
  • Page Numbers: pp.107-116
  • Keywords: Fractional advection-dispersion problem, Laplace transform method, q-fractional homotopy analysis transform technique, Mittage-Leffler function


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.