Owolabi Kolade M, Atangana Abdon
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa.
Chaos. 2019 Feb;29(2):023111. doi: 10.1063/1.5085490.
Mathematical analysis with the numerical simulation of the newly formulated fractional version of the Adams-Bashforth method using the Atangana-Baleanu operator which has both nonlocal and nonsingular properties is considered in this paper. We adopt the fixed point theory and approximation method to prove the existence and uniqueness of the solution via general two-component time fractional differential equations. The method is tested with three nonlinear chaotic dynamical systems in which the integer-order derivative is modeled with the proposed fractional-order case. The simulation result for different α values in (0,1] is presented.
本文考虑了使用具有非局部和非奇异性质的阿坦加纳-巴莱亚努算子对新构造的分数阶亚当斯-巴什福思方法进行数值模拟的数学分析。我们采用不动点理论和近似方法，通过一般的双分量时间分数阶微分方程来证明解的存在性和唯一性。该方法在三个非线性混沌动力系统中进行了测试，其中整数阶导数用所提出的分数阶情况进行建模。给出了在(0,1]范围内不同α值的模拟结果。
