Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space

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摘要

In this paper, approximate solutions to a class of fractional differential equations with delay are presented by using a semi-analytical approach in Hilbert function space. Further, the uniqueness of the solution is proved in the space of real-valued continuous functions, as well as the existence of the solution is proved in Hilbert function space. We also prove convergence and perform an analysis error for the proposed approach. Sophisticated delay differential equations of fractional order are considered as test examples. Numerical results illustrate the efficiency of the proposed approach computationally.

论文关键词:Hilbert function space,Reproducing kernel,Existence,Uniqueness,Convergence

论文评审过程:Received 28 January 2014, Revised 18 May 2015, Accepted 6 June 2015, Available online 20 July 2015, Version of Record 20 July 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2015.06.012