Comparative analysis for fractional nonlinear Sturm-Liouville equations with singular and non-singular kernels
Comparative analysis for fractional nonlinear Sturm-Liouville equations with singular and non-singular kernels
复制标题
奇异核和非奇异核的分数阶非线性 Sturm-Liouville 方程的比较分析
DOI：
10.3934/math.2022736
复制
发表时间：
2022
期刊：
影响因子：
2.2
通讯作者：
Ahu Ercan
中科院分区：
文献类型：
--
作者：
Ahu Ercan
提出了两类非线性分数阶Sturm-Liouville（SL）问题的Laplace-Adomian分解方法（LADM），该方法能产生快速收敛的级数解。分数阶导数定义在Caputo，Conformable，Caputo-Fabrizio的Caputo（CFC），Caputo型Atangana-Baleanu（ABC）意义下。利用这种方法，得到了所研究问题的近似解。从Caputo和ABC导数生成的解由分数阶导数固有的Mittag-Leffler函数表示，并且使用保形和CFC导数获得的解生成双曲正弦和余弦函数。因此，我们得到了分数阶非线性SL方程的一些新的解决方案。分数阶微积分提供了比经典微积分更多的数据，在具有记忆效应的数学建模中得到了广泛的应用。最后，通过不同的p $，$ \lambda $和$ \alpha $阶数下的图，对所考虑问题的新解进行了分析和比较。
This article presents the Laplace-Adomian decomposition method (LADM), which produces a fast convergence series solution, for two types of nonlinear fractional Sturm-Liouville (SL) problems. The fractional derivatives are defined in the Caputo, conformable, Caputo-Fabrizio in the sense of Caputo (CFC), Caputo type Atangana-Baleanu (ABC) senses. With the help of this method, approximate solutions of the investigated problems were obtained. The solutions generated from the Caputo and ABC derivatives are represented by the Mittag-Leffler function, which is intrinsic to fractional derivatives, and the solution obtained using the conformable and CFC derivatives generate the hyperbolic sine and cosine functions. Thus, we derive some novel solutions for fractional-order versions of nonlinear SL equations. The fractional calculus provides more data than classical calculus and has been widely used in mathematical modeling with memory effect. Finally, we analyzed and compared these novel solutions of the considered problems by graphs under different values of $ p $, $ \lambda $ and different orders of $ \alpha $.