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Fractional-order Chelyshkov collocation method for solving variable-order fractional differential equations

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Numerical methods demonstrate convergence and efficiency in solving variable-order fractional differential equations.

To present a numerical method for solving variable-order fractional differential equations (VO-FDEs).
Utilized fractional-order Chelyshkov functions to construct numerical methods.
Considered derivative and integral in Caputo and Riemann-Liouville senses respectively.
Transformed VO-FDEs into algebraic equations using spectral collocation method.
Demonstrated convergence of the proposed method through various examples.
The method shows high efficiency and accuracy compared to recent numerical methods.
Successful applications to various examples of VO-FDEs were achieved.

Al-Sharif et al. (2025) studied this question.

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