[1] Arora, R., Chauhan, A.:
Lie Symmetry Analysis and Some Exact Solutions of $(2+1)$-dimensional KdV-Burgers Equation. International Journal of Applied and Computational Mathematics, 5, 1, 2019, 15, Springer,
DOI 10.1007/s40819-019-0603-5 |
MR 3896708
[2] Baleanu, D., Inc, M., Yusuf, A., Aliyu, A.I.:
Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov-Kuznetsov equation. Nonlinear Analysis: Modelling and Control, 22, 6, 2017, 861-876,
DOI 10.15388/NA.2017.6.9 |
MR 3724625
[3] Baleanu, D., Yusuf, A., Aliyu, A.I.:
Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws. Advances in Difference Equations, 2018, 1, 2018, 46, Springer,
DOI 10.1186/s13662-018-1468-3 |
MR 3757664
[4] Bluman, G.W., Cole, J.D.:
The general similarity solution of the heat equation. Journal of Mathematics and Mechanics, 18, 11, 1969, 1025-1042, JSTOR,
MR 0293257
[5] Bluman, G.W., Kumei, S.:
Use of group analysis in solving overdetermined systems of ordinary differential equations. Journal of Mathematical Analysis and Applications, 138, 1, 1989, 95-105, Academic Press,
DOI 10.1016/0022-247X(89)90322-3 |
MR 0988322
[6] Diethelm, K., Ford, N.J., Freed, A.D.:
A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29, 1-4, 2002, 3-22, Springer,
DOI 10.1023/A:1016592219341 |
MR 1926466
[7] El-Nabulsi, R.A.:
Fractional functional with two occurrences of integrals and asymptotic optimal change of drift in the Black-Scholes model. Acta Mathematica Vietnamica, 40, 4, 2015, 689-703, Springer,
DOI 10.1007/s40306-014-0079-7 |
MR 3412572
[8] Feng, L.L., Tian, S.F., Wang, X.B., Zhang, T.T.:
Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation. Communications in Theoretical Physics, 66, 3, 2016, 321, IOP Publishing,
DOI 10.1088/0253-6102/66/3/321 |
MR 3674580
[9] Gazizov, R.K., Kasatkin, A.A., Lukashchuk, S.Y.: Symmetry properties of fractional diffusion equations. Physica Scripta, 2009, T136, 2009, 014016, IOP Publishing,
[10] Hilfer, R.:
Applications of fractional calculus in physics. 35, 12, 2000, World Scientific,
MR 1890104 |
Zbl 0998.26002
[11] Inc, M., Yusuf, A., Aliyu, A.I., Baleanu, D.:
Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations. Physica A: Statistical Mechanics and its Applications, 496, 2018, 371-383, Elsevier,
DOI 10.1016/j.physa.2017.12.119 |
MR 3759755
[12] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.:
Fractional differential equations: A emergent field in applied and mathematical sciences. Factorization, Singular Operators and Related Problems, 2003, 151-173, Springer,
MR 2001597
[13] Kiryakova, V.S.:
Generalized fractional calculus and applications. 1993, CRC Press,
MR 1265940
[15] Liu, W., Chen, K.:
The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations. Pramana, 81, 3, 2013, 377-384, Springer,
DOI 10.1007/s12043-013-0583-7
[16] Luchko, Y., Gorenflo, R.:
Scale-invariant solutions of a partial differential equation of fractional order. Fractional Calculus and Applied Analysis, 3, 1, 1998, 63-78,
MR 1662409
[17] Lukashchuk, S.Y.:
Conservation laws for time-fractional subdiffusion and diffusion-wave equations. Nonlinear Dynamics, 80, 1--2, 2015, 791-802, Springer,
DOI 10.1007/s11071-015-1906-7 |
MR 3324298
[19] Olver, P.J.:
Applications of Lie groups to differential equations. 107, 2000, Springer Science & Business Media,
MR 0836734
[21] Osler, T.J.:
Leibniz rule for fractional derivatives generalized and an application to infinite series. SIAM Journal on Applied Mathematics, 18, 3, 1970, 658-674, SIAM,
DOI 10.1137/0118059 |
MR 0260942
[22] Pandir, Y., Gurefe, Y., Misirli, E.:
New exact solutions of the time-fractional nonlinear dispersive KdV equation. International Journal of Modeling and Optimization, 3, 4, 2013, 349-351, IACSIT Press,
DOI 10.7763/IJMO.2013.V3.296 |
MR 2928587
[23] Podlubny, I.:
Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. 1998, Elsevier,
MR 1658022
[24] Qin, Ch.Y., Tian, Sh.F., Wang, X.B., Zhang, T.T.:
Lie symmetries, conservation laws and explicit solutions for time fractional Rosenau-Haynam equation. Communications in Theoretical Physics, 67, 2, 2017, 157, IOP Publishing,
MR 3610395
[25] Ray, S.S., Sahoo, S., Das, S.: Formulation and solutions of fractional continuously variable order mass-spring-damper systems controlled by viscoelastic and viscous-viscoelastic dampers. Advances in Mechanical Engineering, 8, 5, 2016, 1-17, SAGE Publications Sage UK: London, England,
[26] Richard, H.: Fractional Calculus: an introduction for physicists. 2014, World Scientific,
[27] Rossikhin, Y.A., Shitikova, M.V.:
Analysis of dynamic behaviour of viscoelastic rods whose rheological models contain fractional derivatives of two different orders. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 81, 6, 2001, 363-376, Wiley Online Library,
DOI 10.1002/1521-4001(200106)81:6<363::AID-ZAMM363>3.0.CO;2-9 |
MR 1834711
[28] Rossikhin, Y.A., Shitikova, M.V.:
Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results. Applied Mechanics Reviews, 63, 1, 2010, 010801(1-52), American Society of Mechanical Engineers,
DOI 10.1115/1.4000563
[29] Sahadevan, R., Bakkyaraj, T.:
Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations. Journal of Mathematical Analysis and Applications, 393, 2, 2012, 341-347, Elsevier,
DOI 10.1016/j.jmaa.2012.04.006 |
MR 2921677
[30] Samko, S.G., Kilbas, A.A., Marichev, O.I.:
Fractional integrals and derivatives: theory and applications. 1993, Gordon and Breach, Switzerland.
MR 1347689
[31] Shang, N., Zheng, B.:
Exact solutions for three fractional partial differential equations by the $(G'/G)$ method. Int. J. Appl. Math, 43, 3, 2013, 114-119,
MR 3113392
[32] Singla, K., Gupta, R.K.:
Space-time fractional nonlinear partial differential equations: symmetry analysis and conservation laws. Nonlinear Dynamics, 89, 1, 2017, 321-331, Springer,
DOI 10.1007/s11071-017-3456-7 |
MR 3663696
[33] Tang, B., He, Y., Wei, L., Zhang, X.:
A generalized fractional sub-equation method for fractional differential equations with variable coefficients. Physics Letters A, 376, 38--39, 2012, 2588-2590, Elsevier,
DOI 10.1016/j.physleta.2012.07.018 |
MR 2961121
[35] Wang, G.W., Liu, X.Q., Zhang, Y.Y.:
Lie symmetry analysis to the time fractional generalized fifth-order KdV equation. Communications in Nonlinear Science and Numerical Simulation, 18, 9, 2013, 2321-2326, Elsevier,
DOI 10.1016/j.cnsns.2012.11.032 |
MR 3042039
[36] Wang, X.B., Tian, S.F., Qin, Ch.Y., Zhang, T.T.:
Lie symmetry analysis, conservation laws and exact solutions of the generalized time fractional Burgers equation. EPL (Europhysics Letters), 114, 2, 2016, 20003, IOP Publishing,
MR 3884385
[37] Wang, X.B., Tian, S.F., Qin, Ch.Y., Zhang, T.T.:
Lie symmetry analysis, conservation laws and analytical solutions of a time-fractional generalized KdV-type equation. Journal of Nonlinear Mathematical Physics, 24, 4, 2017, 516-530, Taylor & Francis,
DOI 10.1080/14029251.2017.1375688 |
MR 3698650
[38] Wang, X.B., Tian, S.F.:
Lie symmetry analysis, conservation laws and analytical solutions of the time-fractional thin-film equation. Computational and Applied Mathematics, 2018, 1-13, Springer,
MR 3885819
[39] Yıldırım, A.: An algorithm for solving the fractional nonlinear Schrödinger equation by means of the homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation, 10, 4, 2009, 445-450, De Gruyter,
[40] Yusuf, A., Aliyu, A.I., Baleanu, D.:
Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers-Huxley equation. Optical and Quantum Electronics, 50, 2, 2018, 94, Springer,
DOI 10.1007/s11082-018-1373-8 |
MR 3739715
[41] Zhang, S.: A generalized Exp-function method for fractional Riccati differential equations. Communications In Fractional Calculus, 1, 2010, 48-51,
[42] Zhang, Y., Mei, J., Zhang, X.:
Symmetry properties and explicit solutions of some nonlinear differential and fractional equations. Applied Mathematics and Computation, 337, 2018, 408-418, Elsevier,
DOI 10.1016/j.amc.2018.05.030 |
MR 3827622
[43] Zhdanov, R.Z.:
Conditional Lie-Backlund symmetry and reduction of evolution equations. Journal of Physics A: Mathematical and General, 28, 13, 1995, 3841, IOP Publishing,
DOI 10.1088/0305-4470/28/13/027 |
MR 1352384