Lie symmetry group, exact solutions and conservation laws for multi-term time fractional differential equations-Reference-Cited by-同舟云学术

Lie symmetry group, exact solutions and conservation laws for multi-term time fractional differential equations

Published:2023 Issue:12 Volume:8 Page:30038-30058
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Yang Miao,Wang Lizhen

Abstract

<abstract><p>In this paper, the time fractional Benjamin-Bona-Mahony-Peregrine (BBMP) equation and time-fractional Novikov equation with the Riemann-Liouville derivative are investigated through the use of Lie symmetry analysis and the new Noether's theorem. Then, we construct their group-invariant solutions by means of Lie symmetry reduction. In addition, the power-series solutions are also obtained with the help of the Erdélyi-Kober (E-K) fractional differential operator. Furthermore, the conservation laws for the time-fractional BBMP equation are established by utilizing the new Noether's theorem.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference40 articles.

1. R. K. Gazizov, N. H. Ibragimov, Lie symmetry analysis of differential equations in finance, Nonlinear Dynam., 17 (1998), 387–407. https://doi.org/10.1023/A:1008304132308

2. H. Liu, J. B. Li, Q. X. Zhang, Lie symmetry analysis and exact explicit solutions for general Burgers' equation, J. Comput. Appl. Math., 228 (2009), 1–9. https://doi.org/10.1016/j.cam.2008.06.009

3. A. Jannelli, M. Ruggieri, M. P. Speciale, Exact and numerical solutions of time-fractional advection-diffusion equation with a nonlinear source term by means of the Lie symmetries, Nonlinear Dynam., 92 (2018), 543–555. https://doi.org/10.1007/s11071-018-4074-8

4. A. Jannelli, M. P. Speciale, Exact and numerical solutions of two-dimensional time-fractional diffusion-reaction equations through the Lie symmetries, Nonlinear Dynam., 105 (2021), 2375–2385. https://doi.org/10.1007/s11071-021-06697-5

5. A. Jannelli, M. Ruggieri, M. P. Speciale, Numerical solutions of space-fractional advection-diffusion equations with nonlinear source term, Appl. Numer. Math., 155 (2020), 93–102. https://doi.org/10.1016/j.apnum.2020.01.016

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