Abstract
This article studies the existence and uniqueness of a weak solution of the time-fractional cancer invasion system with nonlocal diffusion operator. Existence and uniqueness results are ensured by adapting the Faedo-Galerkin method and some a priori estimates. Further, finite element numerical scheme is implemented for the considered system. Finally, various numerical computations are performed along with the convergence analysis of the scheme.
Highlights
In the past few decades, a large number of mathematical models have been applied for biological studies
Finite element methods have become popular for numerical simulations of time-fractional diffusion equations due to their good approximation and feasibility to work with any domains
Esen et al [36] studied the numerical solutions of time-fractional diffusion equations and diffusionwave equations using Galerkin finite element method
Summary
In the past few decades, a large number of mathematical models have been applied for biological studies. Finite element methods have become popular for numerical simulations of time-fractional diffusion equations due to their good approximation and feasibility to work with any domains. Esen et al [36] studied the numerical solutions of time-fractional diffusion equations and diffusionwave equations using Galerkin finite element method. Jin et al [29] analyzed the numerical solutions of multiple time-fractional derivative using the Galerkin finite element method. Fractional models are proposed and used in chemical reactions, propagation phenomena, transport systems, pattern formation processes and spatiotemporal distribution of species [41,42,43,44,45] and references therein In this connection, we are interested to study and analyze the time-fractional cancer invasion model with nonlocal diffusion operator.
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