The purpose of the study is to analyze the time‐fractional reaction‐diffusion equation with nonlocal boundary condition. The proposed model is used to predict the invasion of tumor and its growth. Further, we establish the existence and uniqueness of a weak solution of the proposed model using the Faedo‐Galerkin method and compactness arguments.

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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.

In this article, we study the existence and uniqueness of a weak solution of a degenerate reaction–diffusion parabolic system with variable exponents. This model describes the spread of epidemic diseases with a nonlinear diffusion operator. Copyright © 2013 John Wiley & Sons, Ltd.