Exact solutions of fractional nonlinear equations by generalized bell polynomials and bilinear method
Exact solutions of fractional nonlinear equations by generalized bell polynomials and bilinear method
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DOI：
10.2298/tsci200520036l
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发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Mingshuo Liu;Lijun Zhang;Yong Fang;Huanhe Dong
中科院分区：
文献类型：
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作者：
Mingshuo Liu;Lijun Zhang;Yong Fang;Huanhe Dong
对于大量介于弹性和粘性材料之间的流体，分数阶导数模型比整数阶模型具有更大的优势。基于协调分数导数和各自的有用性质，利用广义Bell多项式和双线性方法得到了时间分数Burgers方程和Boussinesq-Burgers型方程的双线性形式。给出了不同分数阶的扭结孤子解、反扭结孤子解和单孤子解。时间分数阶系统具有时间记忆特性。随着时间分数阶数的增加，出现较高的振荡频率。分数导数增加了在具有不同弹性和粘性材料之间的流体的复杂系统中改善控制性能的可能性。
For numerous fluids between elastic and viscous materials, the fractional derivative models have an advantage over the integer order models. On the basis of conformable fractional derivative and the respective useful properties, the bilinear form of time fractional Burgers equation and Boussinesq-Burgers equations are obtained using the generalized Bell polynomials and bilinear method. The kink soliton solution, anti-kink soliton solution, and the single-soliton solution for different fractional order are derived, respectively. The time fractional order system possesses property of time memory. Higher oscillation frequency appears as the time fractional order increasing. The fractional derivative increases the possibility of improving the control performance in complex systems with fluids between different elastic and viscous materials.