Lie Symmetry and Exact Solutions of Conformable Time Fractional Schamel–Korteweg–De Vries Equation

被引：0

作者：

Kumar R. ^{[1
]}

Bansal A. ^{[2
]}

机构：

[1] Department of Mathematics, MMEC, Maharishi Markandeshwar (Deemed to be University) Mullana, Haryana, Ambala

[2] Department of Mathematics, D.A.V. College for Women, Punjab, Ferozepur

来源：

International Journal of Applied and Computational Mathematics | 2024年 / 10卷 / 3期

基金：

英国科研创新办公室;

关键词：

35C07; 35Q53; 76M60; 83C15; Exact solutions; Lie group analysis method; Schamel–KdV equation; Traveling wave solutions;

D O I：

10.1007/s40819-024-01746-0

中图分类号：

学科分类号：

摘要：

In this current study, a systematic investigation is carried to derive symmetry reductions of conformable time-fractional Schamel–KdV equation via the Lie symmetry method. Using the obtained Lie point symmetries of nonlinear fractional partial differential equation, the symmetry reduction is generated and utilized that for reduction into an ordinary differential equation. Some solutions of the reduced fractional ordinary differential equation are found with two straightforward methods to study its traveling wave solutions and series solutions respectively. The method helps to obtain solutions in the form of trigonometric, hyperbolic and rational functions. Also, we have presented some figures for the obtained explicit solutions that helps us in physical interpretation of equation. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

引用

共 43 条

[1]

Oldham K.B., Spanier J., The fractional calculus, (1974)

[2]

Podlubny I., Fractional Dierential Equations, (1999)

[3]

Hilfer R., Fractional diffusion based on Riemann-Liouville fractional derivatives, J. Phys. Chem. B, 104, pp. 3914-3917, (2000)

[4]

Sousa E., Li C., A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative, Appl. Numer. Math, 90, pp. 22-37, (2015)

[5]

Jumarie G., Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution, J. Appl. Math. and Comput, 24, pp. 31-48, (2007)

[6]

Diethelm K., The analysis of fractional differential equations: An application-oriented exposition using operators of Caputo type, (2004)

[7]

Celik C., Duman M., Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative, J. comput. phys, 231, pp. 1743-1750, (2012)

[8]

Scherer R., Kalla S.L., Tang Y., Huang J., The Grünwald-Letnikov method for fractional differential equations, Comput. Math. with Appl, 62, pp. 902-917, (2011)

[9]

Jumarie G., Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Appl. Math. Lett, 22, pp. 378-385, (2009)

[10]

Kilbas A.A., Srivastava H.M., Trujillo. J.J., : Theory and Applications of Fractional Differential Equations., (2006)

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