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Two-Dimensional Advection–Diffusion Process with Memory and Concentrated Source

1
Abdus Salam School of Mathematical Sciences, Government College University, 5400 Lahore, Pakistan
2
Department of Mathematics, Lahore Leads University, 5400 Lahore, Pakistan
3
Department of Theoretical Mechanics, Technical University “Gheorghe Asachi” of Iasi, 6600 Iasi, Romania
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 879; https://doi.org/10.3390/sym11070879
Received: 25 June 2019 / Revised: 2 July 2019 / Accepted: 3 July 2019 / Published: 4 July 2019
(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)
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Abstract

Two-dimensional advection–diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tail memory (a differential equation with Caputo–Fabrizio time-fractional derivatives). An analytical solution of the initial-boundary value problem has been determined by employing the Laplace transform and double sine-Fourier transforms. A numerical solution of the studied problem has been determined using finite difference approximations. Numerical simulations for both solutions have been carried out using the software Mathcad. View Full-Text
Keywords: Advection–diffusion; fractional derivative; concentrated source; integral transform Advection–diffusion; fractional derivative; concentrated source; integral transform
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Ahmed, N.; Shah, N.A.; Vieru, D. Two-Dimensional Advection–Diffusion Process with Memory and Concentrated Source. Symmetry 2019, 11, 879.

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