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    A collocation method for solving time fractional nonlinear Korteweg-de Vries-Burgers equation arising in shallow water waves
    (World Scientific Publ Co Pte Ltd, 2023) Karaagac, Berat; Esen, Alaattin; Owolabi, Kolade M. M.; Pindza, Edson
    This paper focuses on numerical solutions of time fractional nonlinear Korteweg-de Vries-Burgers equation formulated with Caputo's fractional derivative. For this purpose, a framework of combinations of collocation method with the finite-element method is provided using trigonometric quintic B-spline basis. The method consists of both spatial discretization and temporal discretization using approximate solution and Crank-Nicolson approach. Discretizing fractional derivative is made using L1(0 <= 1) algorithm which is derived from the definition of Caputo derivative using an approximate function. The stability analysis is established using von-Neumann stability technique. The numerical results obtained using the collocation method are presented via tables and graphics. The novel results demonstrate the efficiency and reliability of the method.