Abstract
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.
•The time-fractional convection–diffusion–reaction equation coupled with the Darcy system is considered.•A priori estimates for the solution by employing the method of energy inequalities are established.•Existence, uniqueness and regularity properties of a weak solution are investigated.•The analysis is based on two different methodologies in combination with two alternative variational formulations.