메뉴 건너뛰기




Volumn 182, Issue 2, 2006, Pages 1083-1092

Decomposition method for solving fractional Riccati differential equations

Author keywords

Adomian decomposition method; Fractional derivative; Pad approximants; Riccati equation

Indexed keywords

APPROXIMATION THEORY; NUMBER THEORY; NUMERICAL METHODS; PROBLEM SOLVING; RELIABILITY THEORY; RICCATI EQUATIONS;

EID: 33751512215     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.05.008     Document Type: Article
Times cited : (187)

References (31)
  • 2
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calculus Appl. Anal. 5 (2002) 367-386
    • (2002) Fract. Calculus Appl. Anal. , vol.5 , pp. 367-386
    • Podlubny, I.1
  • 3
    • 33751509999 scopus 로고    scopus 로고
    • J.H. He, Nonlinear oscillation with fractional derivative and its applications, in: International Conference on Vibrating Engineering'98, 1998, Dalian, China, pp. 288-291.
  • 4
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and their approximations
    • He J.H. Some applications of nonlinear fractional differential equations and their approximations. Bull. Sci. Technol. 15 2 (1999) 86-90
    • (1999) Bull. Sci. Technol. , vol.15 , Issue.2 , pp. 86-90
    • He, J.H.1
  • 5
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.167 , pp. 57-68
    • He, J.H.1
  • 6
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • Grigorenko I., and Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett. 91 3 (2003) 034101-034104
    • (2003) Phys. Rev. Lett. , vol.91 , Issue.3 , pp. 034101-034104
    • Grigorenko, I.1    Grigorenko, E.2
  • 7
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: 'Some basic problems in continuum and statistical mechanics'
    • Carpinteri A., and Mainardi F. (Eds), Springer-Verlag, New York
    • Mainardi F. Fractional calculus: 'Some basic problems in continuum and statistical mechanics'. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, New York 291-348
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 9
    • 26444438049 scopus 로고    scopus 로고
    • Pitfalls in fast numerical solvers for fractional differential equations
    • Diethelm K., Ford J.M., Ford N.J., and Weilbeer W. Pitfalls in fast numerical solvers for fractional differential equations. J. Comput. Appl. Math. 186 (2006) 482-503
    • (2006) J. Comput. Appl. Math. , vol.186 , pp. 482-503
    • Diethelm, K.1    Ford, J.M.2    Ford, N.J.3    Weilbeer, W.4
  • 10
    • 33751534006 scopus 로고    scopus 로고
    • R. Gorenflo, Afterthoughts on interpretation of fractional derivatives and integrals, in: P. Rusev, I. Dimovski, V. Kiryakova (Eds.), Transform Methods and Special Functions, Varna 96, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia, 1998, pp. 589-591.
  • 11
    • 33751544036 scopus 로고    scopus 로고
    • A. Luchko, R. Groneflo, The initial value problem for some fractional differential equations with the Caputo derivative, Preprint series A08-98, Fachbreich Mathematik und Informatik, Freic Universitat Berlin, 1998.
  • 14
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J. Roy. Astral. Soc. 13 (1967) 529-539
    • (1967) J. Roy. Astral. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 15
    • 0041185368 scopus 로고
    • A review of the decomposition method in applied mathematics
    • Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135 (1988) 501-544
    • (1988) J. Math. Anal. Appl. , vol.135 , pp. 501-544
    • Adomian, G.1
  • 17
    • 1642290056 scopus 로고    scopus 로고
    • Comparing numerical methods for the solutions of systems of ordinary differential equations
    • Shawagfeh N., and Kaya D. Comparing numerical methods for the solutions of systems of ordinary differential equations. Appl. Math. Lett. 17 (2004) 323-328
    • (2004) Appl. Math. Lett. , vol.17 , pp. 323-328
    • Shawagfeh, N.1    Kaya, D.2
  • 18
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Appl. Math. Comput. 131 2 (2002) 517-529
    • (2002) Appl. Math. Comput. , vol.131 , Issue.2 , pp. 517-529
    • Shawagfeh, N.T.1
  • 19
    • 24144494623 scopus 로고    scopus 로고
    • An explicit and numerical solutions of the fractional KdV equation
    • Momani S. An explicit and numerical solutions of the fractional KdV equation. Math. Comput. Simul. 70 2 (2005) 110-118
    • (2005) Math. Comput. Simul. , vol.70 , Issue.2 , pp. 110-118
    • Momani, S.1
  • 20
    • 27744514614 scopus 로고    scopus 로고
    • Non-perturbative analytical solutions of the space- and time-fractional Burgers equations
    • Momani S. Non-perturbative analytical solutions of the space- and time-fractional Burgers equations. Chaos Solitons & Fractals 28 4 (2006) 930-937
    • (2006) Chaos Solitons & Fractals , vol.28 , Issue.4 , pp. 930-937
    • Momani, S.1
  • 21
    • 33744981446 scopus 로고    scopus 로고
    • Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method
    • Momani S., and Odibat Z. Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method. Appl. Math. Comput. 177 2 (2006) 488-494
    • (2006) Appl. Math. Comput. , vol.177 , Issue.2 , pp. 488-494
    • Momani, S.1    Odibat, Z.2
  • 22
    • 0001100804 scopus 로고    scopus 로고
    • Padè approximants algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain
    • Boyd J. Padè approximants algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput. Phys. 11 3 (1997) 299-303
    • (1997) Comput. Phys. , vol.11 , Issue.3 , pp. 299-303
    • Boyd, J.1
  • 23
    • 7444228191 scopus 로고    scopus 로고
    • Analytical approximate solutions of nonlinear oscillators by the modified decomposition method
    • Momani S. Analytical approximate solutions of nonlinear oscillators by the modified decomposition method. Int. J. Mod. Phys. C 15 (2004) 967-979
    • (2004) Int. J. Mod. Phys. C , vol.15 , pp. 967-979
    • Momani, S.1
  • 24
    • 0002811385 scopus 로고    scopus 로고
    • Analytical approximations and Padé approximants for Volterra's population model
    • Wazwaz A.M. Analytical approximations and Padé approximants for Volterra's population model. Appl. Math. Comput. 100 (1999) 13-25
    • (1999) Appl. Math. Comput. , vol.100 , pp. 13-25
    • Wazwaz, A.M.1
  • 25
    • 84970868898 scopus 로고
    • Convergence of Adomian's method
    • Cherruault Y. Convergence of Adomian's method. Kybernetes 18 (1989) 31-38
    • (1989) Kybernetes , vol.18 , pp. 31-38
    • Cherruault, Y.1
  • 26
    • 0000395259 scopus 로고
    • Decomposition methods: a new proof of convergence
    • Cherruault Y., and Adomian G. Decomposition methods: a new proof of convergence. Math. Comput. Model. 18 (1993) 103-106
    • (1993) Math. Comput. Model. , vol.18 , pp. 103-106
    • Cherruault, Y.1    Adomian, G.2
  • 29
    • 4444374711 scopus 로고    scopus 로고
    • Solving Riccati differential equation using Adomian's decomposition method
    • El-Tawil M.A., Bahnasawi A.A., and Abdel-Naby A. Solving Riccati differential equation using Adomian's decomposition method. Appl. Math. Comput. 157 2 (2004) 503-514
    • (2004) Appl. Math. Comput. , vol.157 , Issue.2 , pp. 503-514
    • El-Tawil, M.A.1    Bahnasawi, A.A.2    Abdel-Naby, A.3
  • 30
    • 31144479330 scopus 로고    scopus 로고
    • Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method
    • Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl. Math. Comput. 172 (2006) 485-490
    • (2006) Appl. Math. Comput. , vol.172 , pp. 485-490
    • Abbasbandy, S.1
  • 31
    • 33751541758 scopus 로고    scopus 로고
    • N.J. Ford, A.C. Simpson, The approximate solution of fractional differential equations of order greater than 1, Numerical Analysis Report 386, Manchester Centre for Numerical Computational Mathematics, 2001.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.