A note on Lie point symmetry to generalized fractional Burgers’ equation

Junior Cesar Alves Soares, Felix Costa Silva, Stefânia Jarosz, Gastão Silves Ferreira Frederico

Resumo


In this article we will present the method developed by [5] to find Lie symmetries for fractional differential equations. In particular, we will find the symmetries for the generalized Burgers equation.


Palavras-chave


Lie Symmetry; Fractional Calculus; Reimann-Liouville

Texto completo:

PDF (English)

Referências


Harry Bateman. “Some recent researches on the motion of fluids”. In: Monthly Weather Review 43.4 (1915), pp. 163–170.

Bibekananda Bira, Tungala Raja Sekhar, and Dia Zeidan. “Exact solutions for some timefractional evolution equations using Lie group theory”. In: Mathematical Methods in the Applied Sciences 41.16 (2018), pp. 6717–6725.

Mayur P Bonkile et al. “A systematic literature review of Burgers’ equation with recent advances”. In: Pramana 90.6 (2018), pp. 1–21.

Igor L Freire. “Note on Lie point symmetries of Burgers Equations”. In: Trends in Computational and Applied Mathematics 11.2 (2010), pp. 151–157.

Raphael K Gazizov, AA Kasatkin, and S Yu Lukashchuk. “Continuous transformation groups of fractional differential equations”. In: Vestnik Usatu 9.3 (2007), p. 21.

RK Gazizov, AA Kasatkin, and S Yu Lukashchuk. “Group-invariant solutions of fractional differential equations”. In: Nonlinear Science and Complexity. Springer, 2011, pp. 51– 59.

Mir Sajjad Hashemi and Dumitru Baleanu. Lie symmetry analysis of fractional differential equations. Chapman and Hall/CRC, 2020.

R Sahadevan and T Bakkyaraj. “Invariant analysis of time fractional generalized Burgers and Korteweg–de Vries equations”. In: Journal of mathematical analysis and applications 393.2 (2012), pp. 341–347.

Muhammad Saqib et al. “On Lie symmetry analysis of nonhomogeneous generalized inviscid and fractional Burgers’ equation”. In: Mathematical Methods in the Applied Sciences 44.11 (2021), pp. 8726–8738.

Junior C. A. Soares. “Cálculo Fracionário e as equações de evolução”. PhD thesis. Unicamp, 2016.

BA Tayyan and AH Sakka. “Symmetries and exact solutions of conformable fractional partial differential equations”. In: Palestine Journal of Mathematics 9.1) (2020).




DOI: https://doi.org/10.5540/03.2022.009.01.0231

Apontamentos

  • Não há apontamentos.


SBMAC - Sociedade de Matemática Aplicada e Computacional
Edifício Medical Center - Rua Maestro João Seppe, nº. 900, 16º. andar - Sala 163 | São Carlos/SP - CEP: 13561-120
 

Normas para publicação | Contato