An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with delay Riesz space fractional derivatives. The temporal orders in considered model are taken as 0 < β 1 2 ⋯ m . problem is first approximated by id="M2"> L difference method on direction, then, Galerkin–Legendre applied spatial discretization. Armed an appropriate form of discrete Grönwall inequalities, stability convergence fully investigated energy estimates. We show that proposed stable has convergent order id="M3"> − exponential rate space. finally provide some numerical experiments to efficacy theoretical results.