In this communication, a familiar physical phenomenon along with a time-dependent concentration source in a one-dimensional fractional differential advection-diffusion has been worked out. The problem is supported with the boundary with initial and boundary conditions. First of all, the results for the nondimensional classical advection-diffusion process are deliberated utilizing the Laplace coupled with finite sine-Fourier transforms analytically. Later on, the analysis is expanded for different fractional operators. The inspection of memory factors is presented through Mathcad. The impacts of the fractional (memory) parameter upon the solute concentration are discussed by making use of Mathcad15. A detailed physical significance of the fractional problem in view of the parameters is studied. It is noted that the decreasing change in concentration is associated with the larger values of noninteger parameter.
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