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The first integral method for some time fractional differential equations. (English) Zbl 1246.35202
Summary: The fractional derivatives in the sense of modified Riemann-Liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations.
35R11Fractional partial differential equations
35A22Transform methods (PDE)
[1]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993)
[2]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[3]Podlubny, I.: Fractional differential equations, (1999)
[4]El-Sayed, A. M. A.; Rida, S. Z.; Arafa, A. A. M.: Exact solutions of fractional-order biological population model, Commun. theor. Phys. (Beijing) 52, 992-996 (2009) · Zbl 1184.92038 · doi:10.1088/0253-6102/52/6/04
[5]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. 58, 2091-2097 (2009) · Zbl 1189.65255 · doi:10.1016/j.camwa.2009.03.043
[6]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. 345, 476-484 (2008) · Zbl 1146.35304 · doi:10.1016/j.jmaa.2008.04.007
[7]Wu, G. C.; Lee, E. W. M.: Fractional variational iteration method and its application, Phys. lett. A 374, 2506-2509 (2010)
[8]Fouladi, F.; Hosseinzadeh, E.; Barari, A.: Highly nonlinear temperature-dependent fin analysis by variational iteration method, Heat transfer res. 41, 155-165 (2010)
[9]Song, L. N.; Zhang, H. Q.: Solving the fractional BBM-Burgers equation using the homotopy analysis method, Chaos solitons fractals 40, 1616-1622 (2009) · Zbl 1198.65205 · doi:10.1016/j.chaos.2007.09.042
[10]Abbasbandy, S.; Shirzadi, A.: Homotopy analysis method for multiple solutions of the fractional Sturm–Liouville problems, Numer. algorithms 54, 521-532 (2010) · Zbl 1197.65096 · doi:10.1007/s11075-009-9351-7
[11]Bararnia, H.; Domairry, G.; Gorji, M.: An approximation of the analytic solution of some nonlinear heat transfer in fin and 3D diffusion equations using HAM, Numer. methods partial differential equations 26, 1-13 (2010) · Zbl 1183.65124 · doi:10.1002/num.20404
[12]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. 12, 581-589 (2008) · Zbl 1170.65332 · doi:http://www.m-hikari.com/ijma/ijma-password-2008/ijma-password9-12-2008/index.html
[13]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 26, 117-124 (2010)
[14]Gepreel, K. A.: The homotopy perturbation method applied to the nonlinear fractional Kolmogorov–petrovskii–piskunov equations, Appl. math. Lett. 24, 1428-1434 (2011) · Zbl 1219.35347 · doi:10.1016/j.aml.2011.03.025
[15]Gupta, P. K.; Singh, M.: Homotopy perturbation method for fractional fornberg–Whitham equation, Comput. math. Appl. 61, 50-254 (2011) · Zbl 1211.65138 · doi:10.1016/j.camwa.2010.10.045
[16]Jumarie, G.: Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order, Appl. math. Lett. 19, 873-880 (2006) · Zbl 1116.35046 · doi:10.1016/j.aml.2005.10.016
[17]Zhang, S.; Zhang, H. Q.: Fractional sub-equation method and its applications to nonlinear fractional pdes, Phys. lett. A 375, 1069-1073 (2011)
[18]Jumarie, G.: Modified Riemann–Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. math. Appl. 51, 1367-1376 (2006) · Zbl 1137.65001 · doi:10.1016/j.camwa.2006.02.001
[19]Feng, Z. S.; Roger, K.: Traveling waves to a Burgers–Korteweg–de Vries-type equation with higher-order nonlinearities, J. math. Anal. appl. 328, 1435-1450 (2007) · Zbl 1119.35075 · doi:10.1016/j.jmaa.2006.05.085
[20]Feng, Z. S.: Traveling wave behavior for a generalized Fisher equation, Chaos solitons fractals 38, 481-488 (2008) · Zbl 1146.35380 · doi:10.1016/j.chaos.2006.11.031
[21]Raslan, K. R.: The first integral method for solving some important nonlinear partial differential equations, Nonlinear. dynam. 53, 281 (2008) · Zbl 1176.35149 · doi:10.1007/s11071-007-9262-x
[22]Lu, B.; Zhang, H. Q.; Xie, F. D.: Travelling wave solutions of nonlinear partial equations by using the first integral method, Appl. math. Comput. 216, 1329-1336 (2010) · Zbl 1191.35090 · doi:10.1016/j.amc.2010.02.028
[23]Taghizadeh, N.; Mirzazadeh, M.; Farahrooz, F.: Exact solutions of the nonlinear Schrödinger equation by the first integral method, J. math. Anal. appl. 374, 549-553 (2011) · Zbl 1202.35308 · doi:10.1016/j.jmaa.2010.08.050
[24]Bourbak, N.: Commutative algebra, (1972)
[25]Golmankhaneh, A. K.; Baleanu, D.: On nonlinear fractional Klein–Gordon equation, Sigal process. 91, 446-451 (2011) · Zbl 1203.94031 · doi:10.1016/j.sigpro.2010.04.016
[26]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. 33, 3107-3113 (2009) · Zbl 1205.35251 · doi:10.1016/j.apm.2008.10.034
[27]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) · Zbl 1206.35248 · doi:10.1155/2010/954674
[28]Song, L. N.; Wang, Q.; Zhang, H. Q.: Rational approximation solution of the fractional Sharma–Tasso–olever equation, J. comput. Appl. math. 224, 210-218 (2009) · Zbl 1157.65074 · doi:10.1016/j.cam.2008.04.033