A time-fractional HIV infection model with nonlinear diffusion

Abstract

This paper deals with a set of three partial differential equations involving time-fractional derivatives and nonlinear diffusion operators. This model helps us to understand the HIV spread and transmission into the patient. First, we prove the existence and uniqueness of weak solutions to the mathematical model. Then, the Galerkin finite element scheme is implemented to approximate the solution of the model. Further, a-priori error bounds and convergence estimates for the fully-discrete problem are derived. The second order convergence for the proposed scheme is also proved. Numerical tests are shown to validate the theoretical studies.

Keywords

• Reaction–diffusion equations
• Time-fractional derivatives
• Faedo–Galerkin approximation
• Priori estimates
• Existence of solutions