Abstract
In this article, the Caputo type variable‐order fractional differentiation is utilized for defining a novel fractional form of the regularized long wave Burgers problem which arises in several physical applications. The third‐kind Chebyshev cardinal functions are generated and some matrix relationships related to them are derived. A numerical procedure dependent on these polynomial cardinal functions is developed for the introduced equation. This scheme converts the primary problem solving into finding an algebraic system solution with low computations using approximating the solution of the equation by the expressed cardinal functions. The accuracy of the presented procedure is investigated in some examples. The presented scheme is straightforward and powerful and can be adopted for many other nonlinear fractional problems.
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