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

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.