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Fractional convection-dispersion equation with conformable derivative approach

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  • Chaudhary, Manish
  • Kumar, Rohit
  • Singh, Mritunjay Kumar

Abstract

In this present work, a well-structured and limit-based derivative definition of fractional derivative term, known as conformable derivative, is employed to develop a local generalized form of time variable fractional convection-dispersion equation (FCDE). The fractional models of convection-dispersion equation have been widely established as more authentic mode to characterize the pollutant transport in geological structures. In this work, models are formulated corresponding to spatial dependency of velocity and dispersion coefficient and also for the temporally varying decay rate, that dealt with more realistic phenomenon of the pollutant transport in groundwater reservoir. Due to the non-linearity of the problem, homotopy analysis method (HAM) is adopted to investigate the complex solutions of FCDE. As the FCDE comprises the classical convection-dispersion equation (CDE) as a special case corresponding to the fractional order α=1, so the obtained solutions are validated by the corresponding numerical solution and exact analytical solution for α=1 and solutions are also verified for different fractional values of α. The effect of conformable derivative order α is properly visible over concentration strength. Hence, this investigation helps to interpret the accurate description of time dependent behaviour of contaminant transport in porous structure.

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  • Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308195
    DOI: 10.1016/j.chaos.2020.110426
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    References listed on IDEAS

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    1. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
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    1. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    3. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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