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Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2020-09-15 , DOI: 10.1088/1572-9494/aba24b P Veeresha 1 , D G Prakasha 2
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2020-09-15 , DOI: 10.1088/1572-9494/aba24b P Veeresha 1 , D G Prakasha 2
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In the present study, we consider the q - homotopy analysis transform method to find the solution for modified Camassa–Holm and Degasperis–Procesi equations using the Caputo fractional operator. Both the considered equations are nonlinear and exemplify shallow water behaviour. We present the solution procedure for the fractional operator and the projected solution procedure gives a rapidly convergent series solution. The solution behaviour is demonstrated as compared with the exact solution and the response is plotted in 2D plots for a diverse fractional-order achieved by the Caputo derivative to show the importance of incorporating the generalised concept. The accuracy of the considered method is illustrated with available results in the numerical simulation. The convergence providence of the achieved solution is established in ##IMG## [http://ej.iop.org/images/0253-6102/72/10/105002/ctpaba24bieqn1.gif] {$\hslash $} -curves for a distinct arbitr...
中文翻译:
使用分数算子修改Camassa–Holm和Degasperis–Procesi方程形式的新颖方法
在本研究中,我们考虑使用Caputo分数算子,通过q-同伦分析变换方法来找到修正的Camassa–Holm和Degasperis–Procesi方程的解。所考虑的两个方程都是非线性的,并举例说明了浅水行为。我们为分数算子提供了求解程序,并且投影的求解程序给出了快速收敛的级数解。与精确解相比,该解的行为得到了证明,并且在Caputo导数实现的不同分数阶的2D图中绘制了响应,从而表明了引入广义概念的重要性。在数值模拟中以可用结果说明了所考虑方法的准确性。所实现解决方案的收敛性在## IMG ## [http:// ej。
更新日期:2020-09-16
中文翻译:
使用分数算子修改Camassa–Holm和Degasperis–Procesi方程形式的新颖方法
在本研究中,我们考虑使用Caputo分数算子,通过q-同伦分析变换方法来找到修正的Camassa–Holm和Degasperis–Procesi方程的解。所考虑的两个方程都是非线性的,并举例说明了浅水行为。我们为分数算子提供了求解程序,并且投影的求解程序给出了快速收敛的级数解。与精确解相比,该解的行为得到了证明,并且在Caputo导数实现的不同分数阶的2D图中绘制了响应,从而表明了引入广义概念的重要性。在数值模拟中以可用结果说明了所考虑方法的准确性。所实现解决方案的收敛性在## IMG ## [http:// ej。