메뉴 건너뛰기




Volumn 61, Issue 9, 2011, Pages 2528-2534

A new analytic solution for fractional chaotic dynamical systems using the differential transform method

Author keywords

Chaotic system; Continuous solution; Differential transform method; Fractional Chen system; Modified differential transform method

Indexed keywords

ADAMS-BASHFORTH; ANALYTIC SOLUTION; CHAOTIC DYNAMICAL SYSTEMS; CHEN SYSTEM; CONTINUOUS SOLUTION; DIFFERENTIAL TRANSFORM METHOD; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; MODIFIED DIFFERENTIAL TRANSFORM METHOD; NEW SOLUTIONS; NONLINEAR DIFFERENTIAL EQUATION; SUB-INTERVAL;

EID: 79955482079     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.02.043     Document Type: Article
Times cited : (42)

References (34)
  • 2
    • 67649319511 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional-order Chen's system
    • H. Zhu, S. Zhou, and Z. He Chaos synchronization of the fractional-order Chen's system Chaos Solitons Fractals 41 2009 2733 2740
    • (2009) Chaos Solitons Fractals , vol.41 , pp. 2733-2740
    • Zhu, H.1    Zhou, S.2    He, Z.3
  • 5
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • C.P. Li, and G. Peng Chaos in Chen's system with a fractional order Chaos Solitons Fractals 22 2004 443 450
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 443-450
    • Li, C.P.1    Peng, G.2
  • 6
    • 33748178408 scopus 로고    scopus 로고
    • Extending synchronization scheme to chaotic fractional-order Chen systems
    • DOI 10.1016/j.physa.2006.03.021, PII S0378437106003530
    • J. Wang, X. Xiong, and Y. Zhang Extending synchronization scheme to chaotic fractional-order Chen systems Physica A 370 2006 279 285 (Pubitemid 44310881)
    • (2006) Physica A: Statistical Mechanics and its Applications , vol.370 , Issue.2 , pp. 279-285
    • Wang, J.1    Xiong, X.2    Zhang, Y.3
  • 7
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • K. Diethelm, and N.J. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 8
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
    • K. Diethelm, N.J. Ford, and A.D. Freed A predictorcorrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 2002 3 22 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 9
    • 27744462122 scopus 로고    scopus 로고
    • Synchronization in fractional-order differential systems
    • T.S. Zhou, and C.P. Li Synchronization in fractional-order differential systems Physica D 212 2005 111 125
    • (2005) Physica D , vol.212 , pp. 111-125
    • Zhou, T.S.1    Li, C.P.2
  • 10
    • 58149216130 scopus 로고    scopus 로고
    • An elementary introduction to the homotopy perturbation method
    • J.-H. He An elementary introduction to the homotopy perturbation method Comput. Math. Appl. 57 2009 410 412
    • (2009) Comput. Math. Appl. , vol.57 , pp. 410-412
    • He, J.-H.1
  • 12
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for non-linear problems
    • J.-H. He A coupling method of a homotopy technique and a perturbation technique for non-linear problems Internat. J. Non-Linear Mech. 35 2000 37 43
    • (2000) Internat. J. Non-Linear Mech. , vol.35 , pp. 37-43
    • He, J.-H.1
  • 13
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • DOI 10.1016/j.chaos.2005.03.006, PII S0960077905002687
    • J.-H. He Application of homotopy perturbation method to nonlinear wave equations Chaos Solitons Fractals 26 2005 695 700 (Pubitemid 40682499)
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.3 , pp. 695-700
    • He, J.-H.1
  • 14
    • 71549148064 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving the space-time fractional advectiondispersion equation
    • A. Yildirim, and H. Koak Homotopy perturbation method for solving the space-time fractional advectiondispersion equation Adv. Water Resour. 32 2009 1711 1716
    • (2009) Adv. Water Resour. , vol.32 , pp. 1711-1716
    • Yildirim, A.1    Koak, H.2
  • 15
    • 77952597982 scopus 로고    scopus 로고
    • Analytical approximate solutions of the fractional convectiondiffusion equation with nonlinear source term by He's homotopy perturbation method
    • S. Momani, and A. Yildirim Analytical approximate solutions of the fractional convectiondiffusion equation with nonlinear source term by He's homotopy perturbation method Int. J. Comput. Math. 87 2010 1057 1065
    • (2010) Int. J. Comput. Math. , vol.87 , pp. 1057-1065
    • Momani, S.1    Yildirim, A.2
  • 16
    • 34247395044 scopus 로고    scopus 로고
    • Homotopy perturbation method for nonlinear partial differential equations of fractional order
    • S. Momani, and Z. Odibat Homotopy perturbation method for nonlinear partial differential equations of fractional order Phys. Lett. A 365 2007 345 350
    • (2007) Phys. Lett. A , vol.365 , pp. 345-350
    • Momani, S.1    Odibat, Z.2
  • 17
    • 35348869861 scopus 로고    scopus 로고
    • Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
    • DOI 10.1016/j.chaos.2006.06.041, PII S0960077906005972
    • Z. Odiba, and S. Momani Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order Chaos Solitons Fractals 36 2008 167 174 (Pubitemid 47576648)
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.1 , pp. 167-174
    • Odibat, Z.1    Momani, S.2
  • 18
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compacton-like solution by variational iteration method
    • DOI 10.1016/j.chaos.2005.10.100, PII S0960077905010799
    • J.-H. He, and X. Wu Construction of solitary solution and compacton-like solution by variational iteration method Chaos Solitons Fractals 29 2006 108 113 (Pubitemid 43063201)
    • (2006) Chaos, Solitons and Fractals , vol.29 , Issue.1 , pp. 108-113
    • He, J.-H.1    Wu, X.-H.2
  • 19
    • 28044441357 scopus 로고    scopus 로고
    • Variational approach to nonlinear problems and a review on mathematical model of electrospinning
    • J.-H. He, and H. Liu Variational approach to nonlinear problems and a review on mathematical model of electrospinning Nonlinear Anal. 63 2005 e919 e929
    • (2005) Nonlinear Anal. , vol.63
    • He, J.-H.1    Liu, H.2
  • 20
    • 34748870677 scopus 로고    scopus 로고
    • Variational iteration method: New development and applications
    • DOI 10.1016/j.camwa.2006.12.083, PII S0898122107005494, Variational Iteration Method for Nonlinear Problems
    • J.-H. He, and X. Wu Variational iteration method: new development and applications Comput. Math. Appl. 54 2007 881 894 (Pubitemid 47488841)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 881-894
    • He, J.-H.1    Wu, X.-H.2
  • 21
    • 70349767158 scopus 로고    scopus 로고
    • Application of variational iteration method to fractional initial-value problems
    • I. Ates, and A. Yildirim Application of variational iteration method to fractional initial-value problems Int. J. Nonlinear Sci. Numer. 10 2009 877 883
    • (2009) Int. J. Nonlinear Sci. Numer. , vol.10 , pp. 877-883
    • Ates, I.1    Yildirim, A.2
  • 22
    • 33746218471 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional differential equations using Adomian decomposition
    • DOI 10.1016/j.cam.2005.10.017, PII S0377042705006278
    • H. Jafari, and V. Daftardar-Gejji Solving a system of nonlinear fractional differential equations using Adomian decomposition J. Comput. Appl. Math. 196 2006 644 651 (Pubitemid 44093887)
    • (2006) Journal of Computational and Applied Mathematics , vol.196 , Issue.2 , pp. 644-651
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 23
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • DOI 10.1016/S0096-3003(01)00167-9, PII S0096300301001679
    • N.T. Shawagfeh Analytical approximate solutions for nonlinear fractional differential equations Appl. Math. Comput. 131 2002 517 529 (Pubitemid 34813503)
    • (2002) Applied Mathematics and Computation , vol.131 , Issue.2-3 , pp. 517-529
    • Shawagfeh, N.T.1
  • 25
    • 56049110221 scopus 로고    scopus 로고
    • Adaptation of homotopy analysis method for the numericanalytic solution of Chen system
    • A.K. Alomari, M.S.M. Noorani, and R. Nazar Adaptation of homotopy analysis method for the numericanalytic solution of Chen system Commun. Nonlinear Sci. Numer. Simul. 14 2009 2336 2346
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2336-2346
    • Alomari, A.K.1    Noorani, M.S.M.2    Nazar, R.3
  • 27
    • 50349091556 scopus 로고    scopus 로고
    • Application of multistage homotopy-perturbation method for the solutions of the Chen system
    • M.S.H. Chowdhury, and I. Hashim Application of multistage homotopy-perturbation method for the solutions of the Chen system Nonlinear Anal. RWA 10 2009 381 391
    • (2009) Nonlinear Anal. RWA , vol.10 , pp. 381-391
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 28
    • 77952008913 scopus 로고    scopus 로고
    • On solving the chaotic Chen system: A new time marching design for the variational iteration method using Adomian's polynomial
    • S.M. Goh, M.S.M. Noorani, and I. Hashim On solving the chaotic Chen system: a new time marching design for the variational iteration method using Adomian's polynomial Numer. Algorithms 54 2010 245 260
    • (2010) Numer. Algorithms , vol.54 , pp. 245-260
    • Goh, S.M.1    Noorani, M.S.M.2    Hashim, I.3
  • 29
    • 77950976377 scopus 로고    scopus 로고
    • Homotopy approach for the hyperchaotic Chen system
    • Ak Alomari, M.S.M. Noorani, and R. Nazar Homotopy approach for the hyperchaotic Chen system Phys. Scr. 81 2010 045005
    • (2010) Phys. Scr. , vol.81 , pp. 045005
    • Alomari, A.1    Noorani, M.S.M.2    Nazar, R.3
  • 30
    • 34250215244 scopus 로고    scopus 로고
    • Solution of fractional differential equations by using differential transform method
    • DOI 10.1016/j.chaos.2006.09.004, PII S0960077906008150
    • A. Arikoglu, and I. Ozkol Solution of fractional differential equations by using differential transform method Chaos Solitons Fractals 34 2007 1473 1481 (Pubitemid 46907585)
    • (2007) Chaos, Solitons and Fractals , vol.34 , Issue.5 , pp. 1473-1481
    • Arikoglu, A.1    Ozkol, I.2
  • 31
    • 39449122795 scopus 로고    scopus 로고
    • Generalized differential transform method: Application to differential equations of fractional order
    • DOI 10.1016/j.amc.2007.07.068, PII S0096300307007916
    • Z. Odibat, S. Momani, and V. Erturk Generalized differential transform method: application to differential equations of fractional order Appl. Math. Comput. 197 2008 467 477 (Pubitemid 351273764)
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.2 , pp. 467-477
    • Odibat, Z.1    Momani, S.2    Erturk, V.S.3
  • 32
    • 69149087769 scopus 로고    scopus 로고
    • Reduced differential transform method for partial differential equations
    • Y. Keskin, and G. Oturanc Reduced differential transform method for partial differential equations Int. J. Nonlinear Sci. Numer. 10 2009 741 749
    • (2009) Int. J. Nonlinear Sci. Numer. , vol.10 , pp. 741-749
    • Keskin, Y.1    Oturanc, G.2
  • 33
    • 77955393855 scopus 로고    scopus 로고
    • The reduced differential transform method: A new approach to fractional partial differential equations
    • Y. Keskin, and G. Oturanc The reduced differential transform method: a new approach to fractional partial differential equations Nonlinear Sci. Lett. A 1 2010 207 217
    • (2010) Nonlinear Sci. Lett. A , vol.1 , pp. 207-217
    • Keskin, Y.1    Oturanc, G.2
  • 34
    • 75349091961 scopus 로고    scopus 로고
    • A multi-step differential transform method and application to non-chaotic or chaotic systems
    • Z. Odibat, C. Bertelle, M.A. Aziz-Alaoui, and G.H.E. Duchamp A multi-step differential transform method and application to non-chaotic or chaotic systems Comput. Math. Appl. 59 2010 1462 1472
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1462-1472
    • Odibat, Z.1    Bertelle, C.2    Aziz-Alaoui, M.A.3    Duchamp, G.H.E.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.