A numerical method for the variable-order fractional functional differential equations (VO-FFDEs) has been developed. This method is based on approximation with shifted Legendre polynomials. The properties of the latter were stated, first. These properties, together with the shifted Gauss-Legendre nodes were then utilized to reduce the VO-FFDEs into a solution of matrix equation. Sequentially, the error estimation of the proposed method was investigated. The validity and efficiency of our method were examined and verified via numerical examples.
Hafez, R., Youssri, Y. (2020). 'Legendre-collocation spectral solver for variable-order fractional functional differential equations', Computational Methods for Differential Equations, 8(1), pp. 99-110. doi: 10.22034/cmde.2019.9465
VANCOUVER
Hafez, R., Youssri, Y. Legendre-collocation spectral solver for variable-order fractional functional differential equations. Computational Methods for Differential Equations, 2020; 8(1): 99-110. doi: 10.22034/cmde.2019.9465
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