Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis
Communications in Mathematics (2019)
- Volume: 27, Issue: 2, page 171-185
- ISSN: 1804-1388
Access Full Article
topAbstract
topHow to cite
topReferences
top- Arora, R., Chauhan, A., 10.1007/s40819-019-0603-5, International Journal of Applied and Computational Mathematics, 5, 1, 2019, 15, Springer, (2019) MR3896708DOI10.1007/s40819-019-0603-5
- Baleanu, D., Inc, M., Yusuf, A., Aliyu, A.I., 10.15388/NA.2017.6.9, Nonlinear Analysis: Modelling and Control, 22, 6, 2017, 861-876, (2017) MR3724625DOI10.15388/NA.2017.6.9
- Baleanu, D., Yusuf, A., Aliyu, A.I., 10.1186/s13662-018-1468-3, Advances in Difference Equations, 2018, 1, 2018, 46, Springer, (2018) MR3757664DOI10.1186/s13662-018-1468-3
- 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, (1969) MR0293257
- Bluman, G.W., Kumei, S., 10.1016/0022-247X(89)90322-3, Journal of Mathematical Analysis and Applications, 138, 1, 1989, 95-105, Academic Press, (1989) MR0988322DOI10.1016/0022-247X(89)90322-3
- Diethelm, K., Ford, N.J., Freed, A.D., 10.1023/A:1016592219341, Nonlinear Dynamics, 29, 1-4, 2002, 3-22, Springer, (2002) MR1926466DOI10.1023/A:1016592219341
- El-Nabulsi, R.A., 10.1007/s40306-014-0079-7, Acta Mathematica Vietnamica, 40, 4, 2015, 689-703, Springer, (2015) MR3412572DOI10.1007/s40306-014-0079-7
- Feng, L.L., Tian, S.F., Wang, X.B., Zhang, T.T., 10.1088/0253-6102/66/3/321, Communications in Theoretical Physics, 66, 3, 2016, 321, IOP Publishing, (2016) MR3674580DOI10.1088/0253-6102/66/3/321
- Gazizov, R.K., Kasatkin, A.A., Lukashchuk, S.Y., Symmetry properties of fractional diffusion equations, Physica Scripta, 2009, T136, 2009, 014016, IOP Publishing, (2009)
- Hilfer, R., Applications of fractional calculus in physics, 35, 12, 2000, World Scientific, (2000) Zbl0998.26002MR1890104
- Inc, M., Yusuf, A., Aliyu, A.I., Baleanu, D., 10.1016/j.physa.2017.12.119, Physica A: Statistical Mechanics and its Applications, 496, 2018, 371-383, Elsevier, (2018) MR3759755DOI10.1016/j.physa.2017.12.119
- 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, (2003) MR2001597
- Kiryakova, V.S., Generalized fractional calculus and applications, 1993, CRC Press, (1993) MR1265940
- Lie, S., 10.1007/BF01446218, Mathematische Annalen, 16, 4, 1880, 441-528, Springer, (1880) MR1510035DOI10.1007/BF01446218
- Liu, W., Chen, K., 10.1007/s12043-013-0583-7, Pramana, 81, 3, 2013, 377-384, Springer, (2013) DOI10.1007/s12043-013-0583-7
- 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, (1998) MR1662409
- Lukashchuk, S.Y., 10.1007/s11071-015-1906-7, Nonlinear Dynamics, 80, 1--2, 2015, 791-802, Springer, (2015) MR3324298DOI10.1007/s11071-015-1906-7
- Noether, E., 10.1080/00411457108231446, Transport Theory and Statistical Physics, 1, 3, 1971, 186-207, Taylor & Francis, (1971) MR0406752DOI10.1080/00411457108231446
- Olver, P.J., Applications of Lie groups to differential equations, 107, 2000, Springer Science & Business Media, (2000) MR0836734
- Ortigueira, M.D., Machado, J.A.T., 10.1016/j.jcp.2014.07.019, Journal of computational Physics, 293, 2015, 4-13, Elsevier, (2015) MR3342452DOI10.1016/j.jcp.2014.07.019
- Osler, T.J., 10.1137/0118059, SIAM Journal on Applied Mathematics, 18, 3, 1970, 658-674, SIAM, (1970) MR0260942DOI10.1137/0118059
- Pandir, Y., Gurefe, Y., Misirli, E., 10.7763/IJMO.2013.V3.296, International Journal of Modeling and Optimization, 3, 4, 2013, 349-351, IACSIT Press, (2013) MR2928587DOI10.7763/IJMO.2013.V3.296
- 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, (1998) MR1658022
- 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, (2017) MR3610395
- 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, (2016)
- Richard, H., Fractional Calculus: an introduction for physicists, 2014, World Scientific, (2014)
- Rossikhin, Y.A., Shitikova, M.V., 10.1002/1521-4001(200106)81:6<363::AID-ZAMM363>3.0.CO;2-9, 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, (2001) MR1834711DOI10.1002/1521-4001(200106)81:6<363::AID-ZAMM363>3.0.CO;2-9
- Rossikhin, Y.A., Shitikova, M.V., 10.1115/1.4000563, Applied Mechanics Reviews, 63, 1, 2010, 010801(1-52), American Society of Mechanical Engineers, (2010) DOI10.1115/1.4000563
- Sahadevan, R., Bakkyaraj, T., 10.1016/j.jmaa.2012.04.006, Journal of Mathematical Analysis and Applications, 393, 2, 2012, 341-347, Elsevier, (2012) MR2921677DOI10.1016/j.jmaa.2012.04.006
- Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional integrals and derivatives: theory and applications, 1993, Gordon and Breach, Switzerland. (1993) MR1347689
- Shang, N., Zheng, B., Exact solutions for three fractional partial differential equations by the method, Int. J. Appl. Math, 43, 3, 2013, 114-119, (2013) MR3113392
- Singla, K., Gupta, R.K., 10.1007/s11071-017-3456-7, Nonlinear Dynamics, 89, 1, 2017, 321-331, Springer, (2017) MR3663696DOI10.1007/s11071-017-3456-7
- Tang, B., He, Y., Wei, L., Zhang, X., 10.1016/j.physleta.2012.07.018, Physics Letters A, 376, 38--39, 2012, 2588-2590, Elsevier, (2012) MR2961121DOI10.1016/j.physleta.2012.07.018
- Tarasov, V.E., 10.1016/j.cnsns.2015.06.007, Communications in Nonlinear Science and Numerical Simulation, 30, 1--3, 2016, 1-4, Elsevier, (2016) MR3420022DOI10.1016/j.cnsns.2015.06.007
- Wang, G.W., Liu, X.Q., Zhang, Y.Y., 10.1016/j.cnsns.2012.11.032, Communications in Nonlinear Science and Numerical Simulation, 18, 9, 2013, 2321-2326, Elsevier, (2013) MR3042039DOI10.1016/j.cnsns.2012.11.032
- 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, (2016) MR3884385
- Wang, X.B., Tian, S.F., Qin, Ch.Y., Zhang, T.T., 10.1080/14029251.2017.1375688, Journal of Nonlinear Mathematical Physics, 24, 4, 2017, 516-530, Taylor & Francis, (2017) MR3698650DOI10.1080/14029251.2017.1375688
- 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, (2018) MR3885819
- 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, (2009)
- Yusuf, A., Aliyu, A.I., Baleanu, D., 10.1007/s11082-018-1373-8, Optical and Quantum Electronics, 50, 2, 2018, 94, Springer, (2018) MR3739715DOI10.1007/s11082-018-1373-8
- Zhang, S., A generalized Exp-function method for fractional Riccati differential equations, Communications In Fractional Calculus, 1, 2010, 48-51, (2010)
- Zhang, Y., Mei, J., Zhang, X., 10.1016/j.amc.2018.05.030, Applied Mathematics and Computation, 337, 2018, 408-418, Elsevier, (2018) MR3827622DOI10.1016/j.amc.2018.05.030
- Zhdanov, R.Z., 10.1088/0305-4470/28/13/027, Journal of Physics A: Mathematical and General, 28, 13, 1995, 3841, IOP Publishing, (1995) MR1352384DOI10.1088/0305-4470/28/13/027