On the Time Fractional Generalized Fisher Equation:Group Similarities and Analytical Solutions
On the Time Fractional Generalized Fisher Equation:Group Similarities and Analytical Solutions
摘要
In this letter,the Lie point symmetries of the time fractional Fisher(TFF) equation have been derived using a systematic investigation.Using the obtained Lie point symmetries,TFF equation has been transformed into a different nonlinear fractional ordinary differential equations with the Erd′elyi–Kober fractional derivative which depends on the parameter α.After that some invariant solutions of underlying equation are reported.
参考文献21
-
1I. Podlubny, Fractional Differential Equations, Academic Press, New York (1999).
-
2A. Kilbas, H. Srivastava, and J. Trujillo, Theory and Applications of Fractional Differential Equations, North- Holland, New York (2006).
-
3R. Fisher, Ann. Eugene. 7 (1937) 335.
-
4D. Frank, Diffusion and Heat Exchange in Chemical Ki- netics, Princeton University Press, Princeton (1955).
-
5J. Canosa, J. Math. Phys. 10 (1969) 1862.
-
6W. Malfiict, Am. 3. Phys. 60 (1992) 650.
-
7D. Aronson and H. Weinberg, Nonlinear Diffusion in Pop- ulation Genetics Combustion and Never Pulse Propaga- tion, Springer, New York (1988).
-
8H. Tuckwell, Introduction to Theoretical Neurobiology, Cambridge University Press, Cambridge (1988).
-
9M. Bramson, Commun. Pure Appl. Math. 31 (1978) 531.
-
10S. Rida, A. El-Sayed, and A. Arafa, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 3847.
-
1H.G.Abdelwahed,E.K.El-Shewy,A.A.Mahmoud.On the Time Fractional Modulation for Electron Acoustic Shock Waves[J].Chinese Physics Letters,2017,34(3):86-89.
-
2JIANG YingJun,MA JingTang.Moving finite element methods for time fractional partial differential equations[J].Science China Mathematics,2013,56(6):1287-1300. 被引量:9
-
3王明新.Wave Fronts of a Generalized Fisher Equation[J].Chinese Science Bulletin,1994,39(16):1326-1328.
-
4Geng Sun,Hua-mo Wu,Li-er Wang.FIRST-ORDER AND SECOND-ORDER, CHAOS-FREE, FINITE DIFFERENCE SCHEMES FOR FISHER EQUATION[J].Journal of Computational Mathematics,2001,19(5):519-530. 被引量:2
-
5黄凤辉,郭柏灵.General solutions to a class of time fractional partial differential equations[J].Applied Mathematics and Mechanics(English Edition),2010,31(7):815-826. 被引量:1
-
6Li-na WANG.Entire Solution of the Degenerate Fisher Equation[J].Acta Mathematicae Applicatae Sinica,2017,33(1):75-82.
-
7段文山,杨红娟,石玉仁.An exact solution of Fisher equation and its stability[J].Chinese Physics B,2006,15(7):1414-1417.
-
8Gepreel Khaled A.Jacobi Elliptic Numerical Solutions for the Time Fractional Variant Boussinesq Equations[J].Journal of Partial Differential Equations,2014,27(3):189-199.
-
9Arzu ■ün,Cevat Kart.Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients[J].Acta Mathematicae Applicatae Sinica,2007,23(4):563-568.
-
10Chun-Yan Qin,Shou-Fu Tian,t Xiu-Bin Wang,Tian-Tian Zhang.Lie Symmetries,Conservation Laws and Explicit Solutions for Time Fractional Rosenau–Haynam Equation[J].Communications in Theoretical Physics,2017,67(2):157-165. 被引量:2