Abstract
In this paper, a variable-order fractional version of the Benney–Lin equation is defined using the variable-order fractional derivative in the Caputo type. A collocation method based on the shifted Jacobi polynomials is applied to deal with this problem. Some matrix relationships related to these polynomials are extracted and used in constructing the established method. The obtained relations cause the method calculations to be significantly reduced, which reduce the method execution time. The established technique converts solving the problem under study into solving an algebraic system of equations. The high accuracy and low computations of the presented scheme are investigated by solving some numerical examples.
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