# Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations

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Osman, Sheelan and Langlands, Trevor. 2022. "Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations." Fractional Calculus and Applied Analysis. 25 (6), pp. 2166-2192. https://doi.org/10.1007/s13540-022-00096-2
Article Title Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations 39668 Article Osman, Sheelan (Author) and Langlands, Trevor (Author) Fractional Calculus and Applied Analysis 25 (6), pp. 2166-2192 27 2022 Germany 1311-0454 https://doi.org/10.1007/s13540-022-00096-2 https://link.springer.com/article/10.1007/s13540-022-00096-2 We consider new numerical schemes to solve two different systems of nonlinear fractional reaction subdiffusion equations. These systems of equations model the reversible reaction A+B⇌C in the presence of anomalous subdiffusion. The first model is based on the Henry \& Wearne [1] model where the reaction term is added to the subdiffusion equation. The second model is based on the model by Angstmann, Donnelly \& Henry [2] which involves a modified fractional differential operator. For both models the Keller Box method [3] along with a modified L1 scheme (ML1), adapted from the Oldham and Spanier L1 scheme [4], are used to approximate the spatial and fractional derivatives respectively. Numerical prediction of both models were compared for a number of examples given the same initial and boundary conditions and the same anomalous exponents. From the results, we see similar short time behaviour for both models predicted. However for long times the solution of the second model remains positive whilst the Henry \& Wearne based–model predictions may become negative. Fractional reaction subdiffusion equation; Keller Box method; Fractional calculus; L1 scheme; Nonlinear reactions systems 490299. Mathematical physics not elsewhere classified 490303. Numerical solution of differential and integral equations 490199. Applied mathematics not elsewhere classified Soran University, Iraq School of Sciences University of Southern Queensland Australian Research Council (ARC)Grant IDARC120 DP130100595

https://research.usq.edu.au/item/q7wz4/numerical-investigation-of-two-models-of-nonlinear-fractional-reaction-subdiffusion-equations

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