A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations

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• 作者：Xiuying Li^a ; ^{lixiuying1112@126.com" class="auth_mail" title="E-mail the corresponding author} ; Boying Wu^b ; ^{mathwby@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Reproducing kernel method ; Variable order ; Fractional order ; Boundary value problems
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：387-393
• 全文大小：412 K

文摘

Based on reproducing kernel theory, a numerical method is proposed for solving variable order fractional boundary value problems for functional differential equations. In the previous works, piecewise polynomial reproducing kernels were employed to solve fractional differential equations. However, the computational cost of fractional order operator acting on such kernel functions is high. In this paper, reproducing kernels with polynomial form will be constructed and applied to solve variable order fractional functional boundary value problems. The method can reduce computation cost and provide highly accurate global approximate solutions.