Botros M, Ziada E A A, El-Kalla I L
Basic Science Departement, Faculty of Engineering, Delta Universiry for Science and Technology, P. O. Box 11152, Mansoura, Egypt.
Nile Higher Institute for Engineering and Technology, Mansoura, Egypt.
Math Biosci Eng. 2022 Sep 13;19(12):13306-13320. doi: 10.3934/mbe.2022623.
In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.
本文采用阿多米安分解法（ADM）和皮卡德技术求解一类具有卡普托 - 法布里齐奥分数阶导数的非线性多维分数阶微分方程。卡普托 - 法布里齐奥分数阶导数的主要优点体现在其卷积型的非奇异核上。得到了保证唯一解的充分条件，讨论了级数解的收敛性，并估计了最大绝对误差。使用这两种技术解决了几个精确解未知的数值问题。给出了两种解之间的对比研究。对比研究表明，与皮卡德技术相比，阿多米安分解法消耗的时间要少得多。
