On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation
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摘要
Recently Caputo and Fabrizio introduced a new derivative with fractional order. In this paper, we presented useful tools about the new derivative and applied it to the nonlinear Fisher’s reaction–diffusion equation. We presented the solution of the modified equation using the notion of iterative method. Using the theory of fixed point, we presented the stability of the used method. Some numerical simulations were presented for different values of fractional order.
论文关键词：Caputo–Fabrizio fractional derivative,New theorems and properties,Nonlinear equation,Fixed point theorem
论文评审过程：Received 18 March 2015, Revised 23 September 2015, Accepted 6 October 2015, Available online 12 November 2015, Version of Record 12 November 2015.
论文官网地址：https://doi.org/10.1016/j.amc.2015.10.021
