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Volumn 218, Issue 6, 2011, Pages 2480-2488

Numerical solution of fractional oscillator equation

Author keywords

Caputo derivative; Convergence; Fractional derivative; Fractional oscillator; Numerical scheme; Riemann Liouville derivative

Indexed keywords

CAPUTO DERIVATIVES; CONVERGENCE; FRACTIONAL DERIVATIVES; FRACTIONAL OSCILLATORS; NUMERICAL SCHEME;

EID: 80053254763     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.07.062     Document Type: Article
Times cited : (48)

References (37)
  • 1
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange equations for fractional variational problems
    • O.P. Agrawal Formulation of Euler-Lagrange equations for fractional variational problems J. Math. Anal. Appl. 272 2002 368 379
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 2
    • 15544379439 scopus 로고    scopus 로고
    • A general formulation and solution scheme for fractional optimal control problems
    • DOI 10.1007/s11071-004-3764-6
    • O.P. Agrawal A general formulation and solution scheme for fractional optimal control problems Nonlinear Dyn. 38 2004 323 337 (Pubitemid 40400624)
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4 , pp. 323-337
    • Agrawal, O.P.1
  • 3
    • 34248181873 scopus 로고    scopus 로고
    • Analytical schemes for a new class of fractional differential equations
    • O.P. Agrawal Analytical schemes for a new class of fractional differential equations J. Phys. A: Math. Theor. 40 2007 5469 5477
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 5469-5477
    • Agrawal, O.P.1
  • 4
    • 34548226960 scopus 로고    scopus 로고
    • A general finite element formulation for fractional variational problems
    • O.P. Agrawal A general finite element formulation for fractional variational problems J. Math. Anal. Appl. 337 2008 1 12
    • (2008) J. Math. Anal. Appl. , vol.337 , pp. 1-12
    • Agrawal, O.P.1
  • 5
    • 76449118673 scopus 로고    scopus 로고
    • Generalized variational problems and Euler-Lagrange equations
    • O.P. Agrawal Generalized variational problems and Euler-Lagrange equations Comput. Math. Appl. 59 2010 1852 1864
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1852-1864
    • Agrawal, O.P.1
  • 6
    • 79960201920 scopus 로고    scopus 로고
    • Generalized variational calculus in terms of multi-parameters fractional derivatives
    • O.P. Agrawal, S.I. Muslih, and D. Baleanu Generalized variational calculus in terms of multi-parameters fractional derivatives Commun. Nonlinear Sci. Numer. Simulat. 16 2011 4756 4767
    • (2011) Commun. Nonlinear Sci. Numer. Simulat. , vol.16 , pp. 4756-4767
    • Agrawal, O.P.1    Muslih, S.I.2    Baleanu, D.3
  • 7
    • 77957362548 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
    • R. Almeida, and D.F.M. Torres Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives Commun. Nonlinear Sci. Numer. Simulat. 16 2011 1490 1500
    • (2011) Commun. Nonlinear Sci. Numer. Simulat. , vol.16 , pp. 1490-1500
    • Almeida, R.1    Torres, D.F.M.2
  • 8
    • 4043139312 scopus 로고    scopus 로고
    • Lagrangians with linear velocities within Riemann-Liouville fractional derivatives
    • D. Baleanu, and T. Avkar Lagrangians with linear velocities within Riemann-Liouville fractional derivatives Nuovo Ciemento B 119 2004 73 79 (Pubitemid 39057448)
    • (2004) Nuovo Cimento della Societa Italiana di Fisica B , vol.119 , Issue.1 , pp. 73-79
    • Baleanu, D.1    Avkar, T.2
  • 9
    • 23344444772 scopus 로고    scopus 로고
    • Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
    • D. Baleanu, and S.I. Muslish Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives Phys. Scripta 72 2005 119 121 (Pubitemid 41101668)
    • (2005) Physica Scripta , vol.72 , Issue.2-3 , pp. 119-121
    • Baleanu, D.1    Muslih, S.I.2
  • 10
    • 33745870156 scopus 로고    scopus 로고
    • Fractional Hamiltonian analysis of irregular systems
    • DOI 10.1016/j.sigpro.2006.02.008, PII S0165168406000508, Fractional Calculus Applications in Signals and Systems
    • D. Baleanu Fractional Hamiltonian analysis of irregular systems Signal Process. 86 2006 2632 2636 (Pubitemid 44026630)
    • (2006) Signal Processing , vol.86 , Issue.10 , pp. 2632-2636
    • Baleanu, D.1
  • 11
    • 42449096849 scopus 로고    scopus 로고
    • On exact solutions of a class of fractional Euler-lagrange equations
    • DOI 10.1007/s11071-007-9281-7
    • D. Baleanu, and D.J.J. Trujillo On exact solutions of a class of fractional Euler-Lagrange equations Nonlinear Dyn. 52 2008 331 335 (Pubitemid 351572392)
    • (2008) Nonlinear Dynamics , vol.52 , Issue.4 , pp. 331-335
    • Baleanu, D.1    Trujillo, J.J.2
  • 12
    • 80053249726 scopus 로고    scopus 로고
    • Fractional Euler-Lagrange equations-numerical solutions and applications of reflection operator
    • T. Blaszczyk, and M. Ciesielski Fractional Euler-Lagrange equations-numerical solutions and applications of reflection operator Sci. Res. Instit. Math. Comput. Sci. 2 9 2010 17 24
    • (2010) Sci. Res. Instit. Math. Comput. Sci. , vol.2 , Issue.9 , pp. 17-24
    • Blaszczyk, T.1    Ciesielski, M.2
  • 13
    • 34047097242 scopus 로고    scopus 로고
    • Fractional embedding of differential operators and Lagrangian systems
    • J. Cresson Fractional embedding of differential operators and Lagrangian systems J. Math. Phys. 48 2007 033504
    • (2007) J. Math. Phys. , vol.48 , pp. 033504
    • Cresson, J.1
  • 15
    • 77953523710 scopus 로고    scopus 로고
    • Fractional variational principles with delay within Caputo derivatives
    • F. Jarad, T. Abdeljawad (Maraaba), and D. Baleanu Fractional variational principles with delay within Caputo derivatives Rep. Math. Phys. 65 2010 17 28
    • (2010) Rep. Math. Phys. , vol.65 , pp. 17-28
    • Jarad, F.1    Abdeljawad, T.2    Baleanu, D.3
  • 17
    • 0035737230 scopus 로고    scopus 로고
    • Fractional sequential mechanics - Models with symmetric fractional derivative
    • DOI 10.1023/A:1013378221617
    • M. Klimek Fractional sequential mechanics-models with symmetric fractional derivative Czech. J. Phys. 51 2001 1348 1354 (Pubitemid 33576189)
    • (2001) Czechoslovak Journal of Physics , vol.51 , Issue.12 , pp. 1348-1354
    • Klimek, M.1
  • 18
    • 0036027310 scopus 로고    scopus 로고
    • Lagrangean and Hamiltonian fractional sequential mechanics
    • DOI 10.1023/A:1021389004982
    • M. Klimek Lagrangian and Hamiltonian fractional sequential mechanics Czech. J. Phys. 52 2002 1247 1253 (Pubitemid 36224481)
    • (2002) Czechoslovak Journal of Physics , vol.52 , Issue.11 , pp. 1247-1253
    • Klimek, M.1
  • 19
    • 71849104907 scopus 로고    scopus 로고
    • Solutions of Euler-Lagrange equations in fractional mechanics
    • P. Kielanowski, A. Odzijewicz, M. Schlichenmaier, T. Voronov (Eds.)
    • M. Klimek, Solutions of Euler-Lagrange equations in fractional mechanics. In: P. Kielanowski, A. Odzijewicz, M. Schlichenmaier, T. Voronov (Eds.), AIP Conference Proceedings 956. XXVI Workshop on Geometrical Methods in Physics, Bialowieza, 2007, pp. 73-78.
    • (2007) AIP Conference Proceedings. XXVI Workshop on Geometrical Methods in Physics, Bialowieza , vol.956 , pp. 73-78
    • Klimek, M.1
  • 21
    • 76449087985 scopus 로고    scopus 로고
    • G-Meijer functions series as solutions for certain fractional variational problem on a finite time interval
    • M. Klimek G-Meijer functions series as solutions for certain fractional variational problem on a finite time interval J. Europeen des Systemes Automatises (JESA) 42 2008 653 664
    • (2008) J. Europeen des Systemes Automatises (JESA) , vol.42 , pp. 653-664
    • Klimek, M.1
  • 22
    • 79951597861 scopus 로고    scopus 로고
    • Existence-uniqueness result for a certain equation of motion in fractional mechanics
    • M. Klimek Existence-uniqueness result for a certain equation of motion in fractional mechanics Bull. Pol. Acad. Sci.: Tech. Sci. 58 2010 573 581
    • (2010) Bull. Pol. Acad. Sci.: Tech. Sci. , vol.58 , pp. 573-581
    • Klimek, M.1
  • 23
    • 76449102581 scopus 로고    scopus 로고
    • On analogues of exponential functions for antisymmetric fractional derivatives
    • M. Klimek On analogues of exponential functions for antisymmetric fractional derivatives Comput. Math. Appl. 59 2010 1709 1717
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1709-1717
    • Klimek, M.1
  • 24
    • 41349098540 scopus 로고    scopus 로고
    • Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form
    • J.S. Leszczynski Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form Phys. Rev. E 70 2004 051315-1 051315-15
    • (2004) Phys. Rev. e , vol.70 , pp. 0513151-05131515
    • Leszczynski, J.S.1
  • 25
    • 80053224218 scopus 로고    scopus 로고
    • Monograph No. 198, Publishing Office of Czestochowa University of Technology, Czestochowa
    • J.S. Leszczynski, An Introduction to Fractional Mechanics, Monograph No. 198, Publishing Office of Czestochowa University of Technology, Czestochowa, 2011.
    • (2011) An Introduction to Fractional Mechanics
    • Leszczynski, J.S.1
  • 26
    • 79958118289 scopus 로고    scopus 로고
    • Modeling the transition between stable and unstable operation while emptying a silo
    • J.S. Leszczynski, and T. Blaszczyk Modeling the transition between stable and unstable operation while emptying a silo Granular Matter 13 2011 429 438
    • (2011) Granular Matter , vol.13 , pp. 429-438
    • Leszczynski, J.S.1    Blaszczyk, T.2
  • 29
    • 14844283120 scopus 로고    scopus 로고
    • Hamiltonian formulation of systems with linear velocities within RiemannLiouville fractional derivatives
    • S.I. Muslih, and D. Baleanu Hamiltonian formulation of systems with linear velocities within RiemannLiouville fractional derivatives J. Math. Anal. Appl. 304 2005 599 603
    • (2005) J. Math. Anal. Appl. , vol.304 , pp. 599-603
    • Muslih, S.I.1    Baleanu, D.2
  • 30
    • 79961009317 scopus 로고    scopus 로고
    • Fractional variational calculus with classical and combined Caputo derivatives
    • doi:10.1016/j.na.2011.01.010: TMA
    • T. Odzijewicz, A.B. Malinowska, D.F.M. Torres, Fractional variational calculus with classical and combined Caputo derivatives, Nonlinear Anal.: TMA, doi:10.1016/j.na.2011.01.010.
    • Nonlinear Anal.
    • Odzijewicz, T.1    Malinowska, A.B.2    Torres, D.F.M.3
  • 35
    • 0034275979 scopus 로고    scopus 로고
    • Fractional calculus and continuous time finance
    • E. Scalas, R. Gorenflo, and F. Mainardi Fractional calculus and continuous time finance Physica A 284 2000 376 384
    • (2000) Physica A , vol.284 , pp. 376-384
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3
  • 36
    • 33748569516 scopus 로고    scopus 로고
    • Computation of fractional order derivative and integral via power series expansion and signal modelling
    • F. Youcef Computation of fractional order derivative and integral via power series expansion and signal modelling Nonlinear Dyn. 46 2006 1 15
    • (2006) Nonlinear Dyn. , vol.46 , pp. 1-15
    • Youcef, F.1


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