We consider the Darcy flow equation coupled with the Caputo time-fractional convection–reaction–diffusion equations. This system describes the concentration distribution of a fluid running through a porous medium. A priori estimates are established for the solution by employing the method of energy inequalities. The existence, uniqueness and regularity properties of a weak solution are studied. Our analysis relies on two novel and different methodologies in combination with two alternative variational formulations.

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