Locally one-dimensional schemes for the diffusion equation with a fractional time derivative in an arbitrary domain

Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method

“…Over the most recent couple of decades, fractional-order differential equations have been effectively utilized for modeling a wide range of processes and systems in the applied sciences and engineering. The basic information on fractional calculus can be found in [1][2][3]. The extensive applications in science and engineering are portrayed by fractional partial differential equation (PDEs) [4][5][6][7][8].…”

“…3 1.9384 × 10 −4 1.2747 × 10 −4 1.6001 × 10 −4 7.7998 × 10 −5 1.1545 × 10 −4 6.2711 × 10 −5 5.0000 × 10 −4 2.6002 × 10 −4 1.6562 × 10 −4 8.7511 × 10 −5 4.0421 × 10 −5 6.6581 × 10 −5 3.0006 × 10 −5 2.5000 × 10 −4 3.1467 × 10 −4 2.1193 × 10 −4 6.2482 × 10 −5 4.1427 × 10 −5 3.7293 × 10 −5 1.7774 × 10 −5…”

Difference schemes for partial differential equations of fractional order

“…In work [29] there were constructed multi-dimensional difference schemes for the fractional order diffusion equation and the convergence of the difference schemes was proved for all , 0 < 1. Work [30] was devoted to considering locally-one-dimensional difference schemes for a fractional order diffusion equation with variable coefficients in domains of a complicated shape. The stability and the uniform convergence of locally-one-dimensional schemes were proved for the considered problem.…”