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# The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative

• *Corresponding author: Yacine Arioua

This work was financially supported by the General Direction of Scientific Research and Technological Development (DGRSDT)-Algeria, PRFU(Grant No. C00L03UN280120180010)

• In this paper, a numerical approximation solution of a space-time fractional diffusion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of different examples.

Mathematics Subject Classification: Primary: 35R11, 65M06, 65M12.

 Citation: • • Figure 1.  Graphical comparison of the numerical and the exact solution with $h = 0.001$, $k = 0.1$, $\rho = 2$, $\alpha = 0.7,$ $n = 20$ and $m = 25$

Figure 2.  Graphical comparison of the numerical and the exact solution with $k = 0.1$, $\rho = 2$, $\alpha = 0.6,$ $\beta = 1.8,$ $n = 30$ and $m = 25$

Figure 3.  Graphical comparison of the numerical and the exact solution with $k = 0.1$, $\rho = 2,$ $\alpha = 0.9$, $(a)\ \beta = 1$, $(b)\ \beta = 2$ and $m = 25$

Figure 4.  Graphical comparison of the numerical and the exact solution with $h = 0.005$, $k = 0.1$, $\rho = 3$, $\alpha = 0.7,$ $n = 20$ and $m = 15$

Figure 5.  Graphical comparison of the numerical and the exact solution with $k = 0.1$, $\rho = 3$, $\alpha = 0.8,$ $\beta = 1.8,$ $n = 40$ and $m = 15$

Figure 6.  Graphical comparison of the numerical and the exact solution with $k = 0.1$, $\rho = 3$, $\alpha = 0.9,$ $(a)\ \beta = 1$, $(b)\ \beta = 2$ and $m = 15$

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