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

Abdus Salam School of Mathematical Sciences, Government College University, 5400 Lahore, Pakistan
Department of Mathematics, Lahore Leads University, 5400 Lahore, Pakistan
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;
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)
PDF [1980 KB, uploaded 4 July 2019]


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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