Application of Newton's polynomial interpolation scheme for variable order fractional derivative with power-law
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai, 600127, India.
Abstract:
This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo-Fabrizio derivative, the Atangana-Baleanu fractal and fractional derivative, and the Atangana-Baleanu Caputo derivative via power-law kernels. Modeling chaotical systems and nonlinear fractional differential equations can be accomplished with the utilization of variable-order differential operators. The computational structures are based on the fractional calculus and Newton's polynomial interpolation. These methods are applied to different variable-order fractional derivatives for Wang-Sun, Rucklidge, and Rikitake systems. We illustrate this novel approach's significance and effectiveness through numerical examples.
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