Fractional KdV and Boussenisq-Burger's equations, reduction to PDE and stability approaches

被引：9

作者：

Abdel-Gawad, H. I. ^{[1
]}

Tantawy, M. ^{[2
]}

Baleanu, D. ^{[3
,4
]}

机构：

[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[2] October 6 Univ, Fac Engn, Dept Basic Sci, Cairo, Egypt

[3] Cankaya Univ, Dept Math, Ankara, Turkey

[4] Inst Space Sci, Magurele, Romania

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 07期

关键词：

reduction to PDE; generalized time-fractional operator; space-time fractional KdV; Boussenisq-Burger's equations; NONLINEAR ROSSBY WAVES; PROPAGATION;

D O I：

10.1002/mma.6178

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The generalized fractional Caputo-operator is discussed. The reduction of partial differential equations retarded or advanced with delays is obtained. The applications to the space-time-fractional KdV and time-fractional Boussenisq-Burger's equation are carried. Semi-self-similar SS wave solutions are obtained. That is, there exists a soliton wave propagates along a specific characteristic curve in the xt- plane. This may be due to the effects associated with the distributed time delay. The effects of space fractional derivative on a system are attributed to the transition states. Thus, anomalous wave transport is produced mainly near the origin.

引用

页码：4125 / 4135

页数：11

共 45 条

[1] Two-layer fluid formation and propagation of periodic solitons induced by (3+1)-dimensional KP equation [J].