Numerical Stability and Convergence for Delay Space-Fractional Fisher Equations with Mixed Boundary Conditions in Two Dimensions

In this paper, for generalized two-dimensional delay space-fractional Fisher equations with mixed boundary conditions, we present the stability and convergence computed by a novel numerical method. The unconditional stability of analytic solutions is first derived. Next, we have established the linear theta-method with the Gr\ddots{u}nwald-Letnikov operator, which has the first-order accuracy in spatial dimensions. Moreover, approaches involved error estimations and inequality reductions are utilized to prove the stability and convergence of numerical solutions under different values of theta. Eventually, we implement a numerical experiment to validate theoretical conclusions, where the interaction impacts of fractional derivatives have been further analyzed by applying two different harmonic operators.