메뉴 건너뛰기




Volumn 395, Issue 2, 2012, Pages 684-693

The first integral method for some time fractional differential equations

Author keywords

Exact solutions; First integral method; Fractional Hirota Satsuma coupled KdV system; Fractional Klein Gordon equation; Fractional Sharma Tasso Olever equation

Indexed keywords


EID: 84864025292     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2012.05.066     Document Type: Article
Times cited : (312)

References (28)
  • 5
    • 70350566604 scopus 로고    scopus 로고
    • Application of He's variational iteration method and Adomian's decomposition method to the fractional KdV-Burgers-Kuramoto equation
    • Safari M., Ganji D.D., Moslemi M. Application of He's variational iteration method and Adomian's decomposition method to the fractional KdV-Burgers-Kuramoto equation. Comput. Math. Appl. 2009, 58:2091-2097.
    • (2009) Comput. Math. Appl. , vol.58 , pp. 2091-2097
    • Safari, M.1    Ganji, D.D.2    Moslemi, M.3
  • 6
    • 43949121726 scopus 로고    scopus 로고
    • The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
    • Inc M. The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method. J. Math. Anal. Appl. 2008, 345:476-484.
    • (2008) J. Math. Anal. Appl. , vol.345 , pp. 476-484
    • Inc, M.1
  • 7
    • 77953478991 scopus 로고    scopus 로고
    • Fractional variational iteration method and its application
    • Wu G.C., Lee E.W.M. Fractional variational iteration method and its application. Phys. Lett. A 2010, 374:2506-2509.
    • (2010) Phys. Lett. A , vol.374 , pp. 2506-2509
    • Wu, G.C.1    Lee, E.W.M.2
  • 8
    • 77951790468 scopus 로고    scopus 로고
    • Highly nonlinear temperature-dependent Fin analysis by variational iteration method
    • Fouladi F., Hosseinzadeh E., Barari A., et al. Highly nonlinear temperature-dependent Fin analysis by variational iteration method. Heat Transfer Res. 2010, 41:155-165.
    • (2010) Heat Transfer Res. , vol.41 , pp. 155-165
    • Fouladi, F.1    Hosseinzadeh, E.2    Barari, A.3
  • 9
    • 65449123574 scopus 로고    scopus 로고
    • Solving the fractional BBM-Burgers equation using the homotopy analysis method
    • Song L.N., Zhang H.Q. Solving the fractional BBM-Burgers equation using the homotopy analysis method. Chaos Solitons Fractals 2009, 40:1616-1622.
    • (2009) Chaos Solitons Fractals , vol.40 , pp. 1616-1622
    • Song, L.N.1    Zhang, H.Q.2
  • 10
    • 77954459409 scopus 로고    scopus 로고
    • Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems
    • Abbasbandy S., Shirzadi A. Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems. Numer. Algorithms 2010, 54:521-532.
    • (2010) Numer. Algorithms , vol.54 , pp. 521-532
    • Abbasbandy, S.1    Shirzadi, A.2
  • 11
    • 73449135842 scopus 로고    scopus 로고
    • An approximation of the analytic solution of some nonlinear heat transfer in Fin and 3D diffusion equations using HAM
    • Bararnia H., Domairry G., Gorji M., et al. An approximation of the analytic solution of some nonlinear heat transfer in Fin and 3D diffusion equations using HAM. Numer. Methods Partial Differential Equations 2010, 26:1-13.
    • (2010) Numer. Methods Partial Differential Equations , vol.26 , pp. 1-13
    • Bararnia, H.1    Domairry, G.2    Gorji, M.3
  • 12
    • 77949497930 scopus 로고    scopus 로고
    • Explicit approximate solution of the coupled KdV equations by using the homotopy analysis method
    • Rashidi M.M., Domairry G., Doosthosseini A., Dinarvand S. Explicit approximate solution of the coupled KdV equations by using the homotopy analysis method. Int. J. Math. Anal. 2008, 12:581-589.
    • (2008) Int. J. Math. Anal. , vol.12 , pp. 581-589
    • Rashidi, M.M.1    Domairry, G.2    Doosthosseini, A.3    Dinarvand, S.4
  • 13
    • 73449083810 scopus 로고    scopus 로고
    • Analytical solution of time-fractional Navier-Stokes equation in polar coordinate by homotopy perturbation method
    • Ganji Z., Ganji D., Ganji A.D., Rostamian M. Analytical solution of time-fractional Navier-Stokes equation in polar coordinate by homotopy perturbation method. Numer. Methods Partial Differential Equations 2010, 26:117-124.
    • (2010) Numer. Methods Partial Differential Equations , vol.26 , pp. 117-124
    • Ganji, Z.1    Ganji, D.2    Ganji, A.D.3    Rostamian, M.4
  • 14
    • 79955470464 scopus 로고    scopus 로고
    • The homotopy perturbation method applied to the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations
    • Gepreel K.A. The homotopy perturbation method applied to the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations. Appl. Math. Lett. 2011, 24:1428-1434.
    • (2011) Appl. Math. Lett. , vol.24 , pp. 1428-1434
    • Gepreel, K.A.1
  • 15
    • 78651257332 scopus 로고    scopus 로고
    • Homotopy perturbation method for fractional Fornberg-Whitham equation
    • Gupta P.K., Singh M. Homotopy perturbation method for fractional Fornberg-Whitham equation. Comput. Math. Appl. 2011, 61:50-254.
    • (2011) Comput. Math. Appl. , vol.61 , pp. 50-254
    • Gupta, P.K.1    Singh, M.2
  • 16
    • 33745108563 scopus 로고    scopus 로고
    • Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order
    • Jumarie G. Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order. Appl. Math. Lett. 2006, 19:873-880.
    • (2006) Appl. Math. Lett. , vol.19 , pp. 873-880
    • Jumarie, G.1
  • 17
    • 79251635229 scopus 로고    scopus 로고
    • Fractional sub-equation method and its applications to nonlinear fractional PDEs
    • Zhang S., Zhang H.Q. Fractional sub-equation method and its applications to nonlinear fractional PDEs. Phys. Lett. A 2011, 375:1069-1073.
    • (2011) Phys. Lett. A , vol.375 , pp. 1069-1073
    • Zhang, S.1    Zhang, H.Q.2
  • 18
    • 33745742268 scopus 로고    scopus 로고
    • Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results
    • Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 2006, 51:1367-1376.
    • (2006) Comput. Math. Appl. , vol.51 , pp. 1367-1376
    • Jumarie, G.1
  • 19
    • 33845905203 scopus 로고    scopus 로고
    • Traveling waves to a Burgers-Korteweg-de Vries-type equation with higher-order nonlinearities
    • Feng Z.S., Roger K. Traveling waves to a Burgers-Korteweg-de Vries-type equation with higher-order nonlinearities. J. Math. Anal. Appl. 2007, 328:1435-1450.
    • (2007) J. Math. Anal. Appl. , vol.328 , pp. 1435-1450
    • Feng, Z.S.1    Roger, K.2
  • 20
    • 42949139271 scopus 로고    scopus 로고
    • Traveling wave behavior for a generalized fisher equation
    • Feng Z.S. Traveling wave behavior for a generalized fisher equation. Chaos Solitons Fractals 2008, 38:481-488.
    • (2008) Chaos Solitons Fractals , vol.38 , pp. 481-488
    • Feng, Z.S.1
  • 21
    • 49049111091 scopus 로고    scopus 로고
    • The first integral method for solving some important nonlinear partial differential equations
    • Raslan K.R. The first integral method for solving some important nonlinear partial differential equations. Nonlinear. Dynam. 2008, 53:281.
    • (2008) Nonlinear. Dynam. , vol.53 , pp. 281
    • Raslan, K.R.1
  • 22
    • 77949914242 scopus 로고    scopus 로고
    • Travelling wave solutions of nonlinear partial equations by using the first integral method
    • Lu B., Zhang H.Q., Xie F.D. Travelling wave solutions of nonlinear partial equations by using the first integral method. Appl. Math. Comput. 2010, 216:1329-1336.
    • (2010) Appl. Math. Comput. , vol.216 , pp. 1329-1336
    • Lu, B.1    Zhang, H.Q.2    Xie, F.D.3
  • 23
    • 77957792961 scopus 로고    scopus 로고
    • Exact solutions of the nonlinear Schrödinger equation by the first integral method
    • Taghizadeh N., Mirzazadeh M., Farahrooz F. Exact solutions of the nonlinear Schrödinger equation by the first integral method. J. Math. Anal. Appl. 2011, 374:549-553.
    • (2011) J. Math. Anal. Appl. , vol.374 , pp. 549-553
    • Taghizadeh, N.1    Mirzazadeh, M.2    Farahrooz, F.3
  • 25
    • 78049333706 scopus 로고    scopus 로고
    • On nonlinear fractional Klein-Gordon equation
    • Golmankhaneh A.K., Baleanu D. On nonlinear fractional Klein-Gordon equation. Sigal Process. 2011, 91:446-451.
    • (2011) Sigal Process. , vol.91 , pp. 446-451
    • Golmankhaneh, A.K.1    Baleanu, D.2
  • 26
    • 61449224678 scopus 로고    scopus 로고
    • Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique
    • Ganji Z.Z., Ganji D.D., Rostamiyan Y. Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique. Appl. Math. Model. 2009, 33:3107-3113.
    • (2009) Appl. Math. Model. , vol.33 , pp. 3107-3113
    • Ganji, Z.Z.1    Ganji, D.D.2    Rostamiyan, Y.3
  • 27
    • 84858112048 scopus 로고    scopus 로고
    • Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique
    • Article 954674
    • Shateri Majid, Ganji D.D. Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique. Int. J. Differ. Equ. 2010, 2010. Article 954674.
    • (2010) Int. J. Differ. Equ. , vol.2010
    • Shateri, M.1    Ganji, D.D.2
  • 28
    • 56449093058 scopus 로고    scopus 로고
    • Rational approximation solution of the fractional Sharma-Tasso-Olever equation
    • Song L.N., Wang Q., Zhang H.Q. Rational approximation solution of the fractional Sharma-Tasso-Olever equation. J. Comput. Appl. Math. 2009, 224:210-218.
    • (2009) J. Comput. Appl. Math. , vol.224 , pp. 210-218
    • Song, L.N.1    Wang, Q.2    Zhang, H.Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.