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Volumn 14, Issue 6, 2013, Pages 363-366

Exp-function method for fractional differential equations

Author keywords

exp function method; fractional complex transform; local fractional calculus; modified Riemann Liouville derivative; nonlinear dispersive equations; Phi four equation

Indexed keywords


EID: 84887314286     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/ijnsns-2011-0132     Document Type: Article
Times cited : (119)

References (31)
  • 1
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Soliton. Fract., 30(2006) 700-708
    • (2006) Chaos Soliton. Fract , vol.30 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 2
    • 34748862326 scopus 로고    scopus 로고
    • Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method
    • X.H. Wu, J.H. He, Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method, Comput. Math. Applicat., 54(2007) 966-986
    • (2007) Comput. Math. Applicat , vol.54 , pp. 966-986
    • Wu, X.H.1    He, J.H.2
  • 3
    • 50949112266 scopus 로고    scopus 로고
    • An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering
    • J.H. He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B, 22(2008) 3487-3578
    • (2008) Int. J. Mod. Phys. B , vol.22 , pp. 3487-3578
    • He, J.H.1
  • 4
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20(2006) 1141-1199
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 5
    • 79953764335 scopus 로고    scopus 로고
    • An Exp-function method for new N-soliton solutions with arbitrary functions of a (2+1)-dimensional vcBK system
    • S. Zhang, H.Q. Zhang, An Exp-function method for new N-soliton solutions with arbitrary functions of a (2+1)-dimensional vcBK system, Comput. Math. Applicat., 61(2011) 1923-1930
    • (2011) Comput. Math. Applicat , vol.61 , pp. 1923-1930
    • Zhang, S.1    Zhang, H.Q.2
  • 7
    • 36248983300 scopus 로고    scopus 로고
    • Exact solutions for a class of nonlinear partial differential equations using exp-function method
    • A. Bekir, A. Boz, Exact Solutions for a Class of Nonlinear Partial Differential Equations using Exp-Function Method, Int. J. Nonlinear Sci. Num., 8(2007) 505-512
    • (2007) Int. J. Nonlinear Sci. Num , vol.8 , pp. 505-512
    • Bekir, A.1    Boz, A.2
  • 8
    • 76649088051 scopus 로고    scopus 로고
    • Solutions for the double Sine-Gordon equation by Exp-function, Tanh, and extended Tanh methods
    • G. Domairry, A.G. Davodi, A.G. Davodi, Solutions for the double Sine-Gordon equation by Exp-function, Tanh, and extended Tanh methods, Numer. Meth. Part. D. E., 26(2010) 384-398
    • (2010) Numer. Meth. Part D.E.26 , pp. 384-398
    • Domairry, G.1    Davodi, A.G.2    Davodi, A.G.3
  • 9
    • 78650141045 scopus 로고    scopus 로고
    • Exact solutions for nonlinear partial differential equations via Exp-function method
    • D. E., 26
    • H. Aminikhah, H. Moosaei, M. Hajipour, Exact solutions for nonlinear partial differential equations via Exp-function method, Numer. Meth. Part. D. E., 26(2010) 1427-1433
    • (2010) Numer. Meth. Part , pp. 1427-1433
    • Aminikhah, H.1    Moosaei, H.2    Hajipour, M.3
  • 10
    • 63449135805 scopus 로고    scopus 로고
    • Explicit analytical solutions of the generalized Burger and Burger-Fisher equations by homotopy perturbation method
    • M.M. Rashidi, D.D. Ganji, S. Dinarvand, Explicit analytical solutions of the generalized Burger and Burger-Fisher equations by homotopy perturbation method, Numer. Meth. Part. D. E., 25(2009) 409-417
    • (2009) Numer. Meth. Part , vol.D. E. , Issue.25 , pp. 409-417
    • Rashidi, M.M.1    Ganji, D.D.2    Dinarvand, S.3
  • 11
    • 84869494625 scopus 로고    scopus 로고
    • Asymptotic methods for solitary solutions and compactons
    • Article ID 916793
    • J.H. He, Asymptotic methods for solitary solutions and compactons, Abstract and Applied Analysis, 2012, Article ID 916793
    • (2012) Abstract and Applied Analysis
    • He, J.H.1
  • 13
    • 79251514418 scopus 로고    scopus 로고
    • The Exp-function method to solve the generalized burgers-fisher equation
    • E. Misirli, Y. Gurefe, The Exp-function Method to Solve the Generalized Burgers-Fisher Equation, Nonlinear Science Letters A, 1(2010) 323-328
    • (2010) Nonlinear Science Letters A , vol.1 , pp. 323-328
    • Misirli, E.1    Gurefe, Y.2
  • 14
    • 79251611305 scopus 로고    scopus 로고
    • A generalized exp-function method for fractional riccati differential equations
    • S. Zhang, Q.A. Zong, D. Liu, Q. Gao, A Generalized Exp-Function Method for Fractional Riccati Differential Equations, Communications in Fractional Calculus, 1(2010) 48-51
    • (2010) Communications in Fractional Calculus , vol.1 , pp. 48-51
    • Zhang, S.1    Zong, Q.A.2    Liu, D.3    Gao, Q.4
  • 16
    • 80051802242 scopus 로고    scopus 로고
    • Analytical and numerical methods in engineering and applied sciences
    • D.D. Ganji, Seyed H. Hashemi Kachapi, Analytical and Numerical Methods in Engineering and Applied Sciences, Progress in Nonlinear Science, 3(2011) 1-579
    • (2011) Progress in Nonlinear Science , vol.3 , pp. 1-579
    • Ganji, D.D.1    Seyed, H.2    Kachapi, H.3
  • 17
    • 84555221318 scopus 로고    scopus 로고
    • Local fractional integral transforms
    • X.J. Yang, Local fractional integral transforms, Progress in Nonlinear Science, 4(2011) 1-225
    • (2011) Progress in Nonlinear Science , vol.4 , pp. 1-225
    • Yang, X.J.1
  • 18
    • 84887276149 scopus 로고    scopus 로고
    • Local fractional functional analysis its applications asian academic publisher limited Hong Kong
    • X.J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong, China, 2011
    • (2011) China
    • Yang, X.J.1
  • 20
    • 84879324154 scopus 로고    scopus 로고
    • Fractal heat conduction problem solved by local fractional variation iteration method
    • Doi: 10.2298/TSCI121124216Y.
    • X.J. Yang, D. Baleanu, Fractal heat conduction problem solved by local fractional variation iteration method, Thermal Science, 2012, Doi: 10.2298/TSCI121124216Y.
    • (2012) Thermal Science
    • Yang, X.J.1    Baleanu, D.2
  • 21
    • 33745742268 scopus 로고    scopus 로고
    • Modified riemann-liouville derivative and fractional taylor series of non-differentiable functions further results
    • G. Jumarie, Modified Riemann-Liouville Derivative and Fractional Taylor series of Non-differentiable Functions Further Results, Computers and Mathematics with Applications, 51(2006) 1367-1376
    • (2006) Computers and Mathematics with Applications , vol.51 , pp. 1367-1376
    • Jumarie, G.1
  • 22
    • 79955145165 scopus 로고    scopus 로고
    • A new fractal derivation
    • J.H. He, A new fractal derivation, Thermal Science, 15(2011) S145-S147
    • (2011) Thermal Science , vol.15
    • He, J.H.1
  • 23
    • 84871448093 scopus 로고    scopus 로고
    • Fractal derivative model for air permeability in hierarchic porous media
    • J. Fan, J.H. He, Fractal derivative model for air permeability in hierarchic porous media, Abstract and Applied Analysis, 2012, 354701
    • (2012) Abstract and Applied Analysis , pp. 354701
    • Fan, J.1    He, J.H.2
  • 24
    • 84874783648 scopus 로고    scopus 로고
    • Biomimic design of multi-scale fabric with efficient heat transfer property
    • J. Fan, J.H. He, Biomimic design of multi-scale fabric with efficient heat transfer property, Thermal Science, 16(5)(2012) 1349-1352
    • (2012) Thermal Science , vol.16 , Issue.5 , pp. 1349-1352
    • Fan, J.1    He, J.H.2
  • 25
    • 79955470495 scopus 로고    scopus 로고
    • Fractional complex transform for fractional differential equations
    • Z.B. Li, J.H. He, Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15(2010) 970-973
    • (2010) Mathematical and Computational Applications , vol.15 , pp. 970-973
    • Li, Z.B.1    He, J.H.2
  • 27
    • 84868613849 scopus 로고    scopus 로고
    • Converting fractional differential equations into partial differential equations
    • J.H. He, Z.B. Li, Converting fractional differential equations into partial differential equations, Thermal Science, 16(2)(2012) 331-334
    • (2012) Thermal Science , vol.16 , Issue.2 , pp. 331-334
    • He, J.H.1    Li, Z.B.2
  • 28
    • 84868609962 scopus 로고    scopus 로고
    • Exact solutions of time-fractional heat conduction equation by the fractional complex transform
    • Z.B. Li, W.H. Zhu, J.H. He, Exact solutions of time-fractional heat conduction equation by the fractional complex transform, Thermal Science, 16(2)(2012) 335-338
    • (2012) Thermal Science , vol.16 , Issue.2 , pp. 335-338
    • Li, Z.B.1    Zhu, W.H.2    He, J.H.3
  • 29
    • 84863370700 scopus 로고    scopus 로고
    • Fractional model for heat conduction in polar bear hairs
    • Q.L. Wang, J.H. He, Z.B. Li, Fractional model for heat conduction in polar bear hairs, Thermal Science, 16(2)(2012) 339-342
    • (2012) Thermal Science , vol.16 , Issue.2 , pp. 339-342
    • Wang, Q.L.1    He, J.H.2    Li, Z.B.3
  • 30
    • 84855203771 scopus 로고    scopus 로고
    • Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus
    • J.H. He, S.K. Elagan, Z.B. Li, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Phys. Lett. A, 376(4)(2012), 257-259
    • (2012) Phys. Lett. A , vol.376 , Issue.4 , pp. 257-259
    • He, J.H.1    Elagan, S.K.2    Li, Z.B.3
  • 31
    • 84884837318 scopus 로고    scopus 로고
    • Local fractional variational iteration method for fractal heat transfer in silk cocoon hierarchy
    • J.H. He, F.J. Liu, Local fractional variational iteration method for fractal heat transfer in silk cocoon hierarchy, Nonlinear Science Letters A, 4(2013) 15-20.
    • (2013) Nonlinear Science Letters A , vol.4 , pp. 15-20
    • He, J.H.1    Liu, F.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.