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A predictor-corrector scheme for the nonlinear chaotic variable-order fractional three-dimensional system. (English) Zbl 1524.65703

Summary: This paper aims to study two-step fractional Adams-Bashforth-Moulton scheme for solving nonlinear fractional variable order differential equations. The fractional derivative used in this paper is the Hadamard fractional derivative. The predictor-corrector scheme is applied for the numerical solution of fractional variable-order chaotic systems. The illustrate scheme reduces these nonlinear fractional variable order differential equations to a system of algebraic equations and then this system will be solved numerically by recursive scheme. Several numerical examples are reported to show the applicability and validity of the illustrated scheme.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
34A08 Fractional ordinary differential equations
65L99 Numerical methods for ordinary differential equations
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