A Reliable Algorithm for Multi-Dimensional Mobile/ Immobile Advection-Dispersion Equation with Variable Order Fractional

Iman I  Gorial

doi:10.17485/ijst/2018/v11i30/127486

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A Reliable Algorithm for Multi-Dimensional Mobile/ Immobile Advection-Dispersion Equation with Variable Order Fractional

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2018/v11i30/127486

Year: 2018, Volume: 11, Issue: 30, Pages: 1-9

Original Article

A Reliable Algorithm for Multi-Dimensional Mobile/ Immobile Advection-Dispersion Equation with Variable Order Fractional

Iman I. Gorial^*

Department of Materials Engineering, University of Technology, Iraq; [email protected]

^*Author for correspondence
Iman I. Gorial,
Department of Materials Engineering, University of Technology, Iraq; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: Presented a modified treatment of initial boundary value problems for multi-dimensional mobile/immobile advection-dispersion equation with variable order fractional (MDMADEVF). Methods: we applied mixed initial and boundary conditions together using variational iteration method (VIM) to get a new initial solution at every iteration. Findings: The simulation results show the proposed system accurate and the utilized algorithm simple and easy to implement. Application: numerical examples were provided to show that variational iteration method was computationally efficient. The results were presented in tables and figures using the MathCAD 12 and Matlab software package when it is needed.

Keywords: Caputo Derivatives, Fractional Mobile / Immobile Advection-Dispersion Model