Mathematical analysis with numerical application of the newly formulated fractional version of the Adams-Bashforth method using the Atangana-Baleanu derivative which has 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. Simulation result for different $\alpha$ values in $(0,1]$ is presented.
翻译:本文将考虑采用具有非本地和非本地特性的阿坦加纳-巴莱阿努衍生物的阿坦加纳-巴什福思方法新配制分数版的数学分析。我们采用固定点理论和近似方法,通过一般的两部分时间偏差方程来证明解决办法的存在和独特性。该方法由三种非线性混乱动态系统测试,其中整数序列衍生物与拟议的分数顺序立案建模。提出了以美元(0,1美元)计算不同价值的模拟结果。