References
- Podlubny I. Fractional differential equations. San Diego (CA): Academic Press; 1999.
- Bagley RL, Torvik PJ. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol. 1983;27:201–210.
- Bagley RL, Torvik PJ. On the fractional calculus model of viscoelastic behavior. J Rheol. 1986;30:133–155.
- Duan ZH, Xiao-Jun YA, Srivastava HM. On the fractal heat transfer problems with local fractional calculus. Therm Sci. 2015;19:1867–1871.
- Sabatier JA, Agrawal OP, Machado JT. Advances in fractional calculus. Dordrecht: Springer; 2007.
- Wharmby AW. A fractional calculus model of anomalous dispersion of acoustic waves. J Acoust Soc Am. 2016;140:2185–2191.
- Kleinz M, Osler TJ. A child's garden of fractional derivatives. Coll Math J. 2000;31:82–88.
- Ortigueira MD, Machado JA. Fractional signal processing and applications. Signal Process. 2003;83:2285–2286.
- Mathieu B, Melchior P, Oustaloup A, et al. Fractional differentiation for edge detection. Signal Process. 2003;83:2421–2432.
- Katugampola UN. A new approach to generalized fractional derivatives. Bull Math Anal Appl. 2014;6:1–5.
- Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of non differentiable functions further results. Comput Math Appl. 2006;51:1367–1376.
- Ortigueira MD, Machado JT. What is a fractional derivative?. J Comput Phys. 2015;293:4–13.
- Zhang Y. A finite difference method for fractional partial differential equation. Appl Math Comput. 2009;215:524–529.
- Yuste SB, Acedo L. An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. SIAM J Numer Anal. 2005;42:1862–1874.
- Odibat Z, Momani S. A generalized differential transform method for linear partial differential equations of fractional order. Appl Math Lett. 2008;21:194–199.
- Gazizov RK, Kasatkin AA. Construction of exact solutions for fractional order differential equations by the invariant subspace method. Comput Math Appl. 2013;66:576–584.
- Choudhary S S, Daftardar-Gejji V. Invariant subspace method: a tool for solving fractional partial differential equations. Fract Calc Appl Anal. 2017;20:477–493.
- Wu GC, Lee EW. Fractional variational iteration method and its application. Phys Lett A. 2010;374:2506–2509.
- Olver PJ. Applications of lie groups to differential equations. New York (NY): Springer; 1986.
- Bluman GW, Anco SC. Symmetries and integration methods for differential equations. New York (NY): Springer-Verlag; 2002.
- Gupta RK, Kaur J. On explicit exact solutions of variable-coefficient time-fractional generalized fifth-order korteweg-de vries equation. Eur Phys J Plus. 2019;134:291.
- Gazizov RK, Kasatkin AA, Lukashchuk SY. Symmetries and group-invariant solutions of nonlinear fractional differential equations, In Proc. Int. Workshop on New Trends in Science and Technology, 2008.
- Bira B, Sekhar TR, Zeidan D. Exact solutions for some time-fractional evolution equations using lie group theory. Math Method Appl Sci. 2018;41:6717–6725.
- Gupta RK, Singla K. Symmetry analysis of variable-coefficient time-fractional nonlinear systems of partial differential equations. Theor Math Phys. 2018;197:1737–1754.
- Kaur J, Gupta RK, Kumar S. On explicit exact solutions and conservation laws for time fractional variable – coefficient coupled Burger's equations. Commun Nonlinear Sci Numer Simul. 2020;83:105108.
- Kawahara T. Oscillatory solitary waves in dispersive media. J Phys Soc Jpn. 1972;33:260–264.
- Liu H, Li J, Liu L. Lie symmetry analysis optimal systems and exact solutions to the fifth-order KdV types of equations. J Math Anal Appl. 2010;368:551–558.
- Badali AH, Hashemi MS, Ghahremani M. Lie symmetry analysis for Kawahara-KdV equations. Comput Methods Differ Equ. 2013;1:135–145.
- Kaur L, Gupta RK. Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized G′/G-expansion method. Math Method Appl Sci. 2013;36:584–600.
- Saldır O, Sakar MG, Erdogan F. Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate. Comp Appl Math. 2019;38:198.
- Bhatter S, Mathur A, Kumar D, et al. Fractional modified Kawahara equation with Mittag–Leffler law. Chaos Solitons Fractals. 2020;131:109508.
- Anco SC, Bluman G. Direct construction method for conservation laws of partial differential equations part I: examples of conservation law classifications. Eur J Appl Math. 2002;13:545–566.
- Naz R. Conservation laws for a complexly coupled KdV system coupled Burgers' system and Drinfeld–Sokolov–Wilson system via multiplier approach. Commun Nonlinear Sci Numer Simul. 2010;15:1177–1182.
- Kara AH, Mahomed FM. Relationship between symmetries and conservation laws. Int J Theor Phys. 2000;39:23–40.
- Naz R, Mahomed FM, Mason DP. Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics. Appl Math Comput. 2008;205:212–230.
- Noether E. Invariant variation problems. Transp Theory Stat Phys. 1971;1:186–207.
- Ibragimov NH. A new conservation theorem. J Math Anal Appl. 2007;333:311–328.
- Malinowska AB. A formulation of the fractional noether-type theorem for multidimensional Lagrangians. Appl Math Lett. 2012;25:1941–1946.
- Frederico GS, Torres DF. A formulation of noether's theorem for fractional problems of the calculus of variations. J Math Anal Appl. 2007;334:834–846.
- Lukashchuk SY. Conservation laws for time-fractional subdiffusion and diffusion-wave equations. Nonlinear Dyn. 2015;80:791–802.
- Sahadevan R, Bakkyaraj T. Invariant analysis of time fractional generalized Burgers and korteweg-de vries equations. J Math Anal Appl. 2012;393:341–347.
- Singla K, Gupta RK. Generalized lie symmetry approach for fractional order systems of differential equations. III. J Math Phys. 2017;58:061501.
- Gazizov RK, Kasatkin AA, Lukashchuk SY. Symmetry properties of fractional diffusion equations. Physica Scripta. 2009;T136:014016.
- Al-Saqabi B, Kiryakova VS. Explicit solutions of fractional integral and differential equations involving Erdélyi-Kober operators. Appl Math Comput. 1998;95:1–13.
- Ibragimov NH. Nonlinear self-adjointness and conservation laws. J Phys A Math Theor. 2011;44:432002.
- Freire IL, C.Sampaio J. Nonlinear self-adjointness of a generalized fifth-order KdV equation. J Phys A Math Theor. 2011;45:032001.
- Agrawal OP. Formulation of Euler–Lagrange equations for fractional variational problems. J Math Anal Appl. 2002;272:368–379.