메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

New applications of the variational iteration method-From differential equations to q-Fractional difference equations

Author keywords

Fractional calculus; Laplace transform; Q calculus; Symbolic computation; Time scales; Variational iteration method

Indexed keywords


EID: 84876541890     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2013-21     Document Type: Article
Times cited : (66)

References (51)
  • 3
    • 77649311766 scopus 로고    scopus 로고
    • Linear sequential q-difference equations of fractional order
    • Mansour, Z: Linear sequential q-difference equations of fractional order. Fract. Calc. Appl. Anal. 12, 159-178 (2009)
    • (2009) Fract. Calc. Appl. Anal. , vol.12 , pp. 159-178
    • Mansour, Z.1
  • 4
    • 77952557731 scopus 로고    scopus 로고
    • Modeling with fractional difference equations
    • Atici, FM, Senguel, S: Modeling with fractional difference equations. J. Math. Anal. Appl. 369, 1-9 (2010)
    • (2010) J. Math. Anal. Appl. , vol.369 , pp. 1-9
    • Atici, F.M.1    Senguel, S.2
  • 5
    • 77956177561 scopus 로고    scopus 로고
    • Common aspects of q-deformed lie algebras and fractional calculus
    • Herrmann, R: Common aspects of q-deformed Lie algebras and fractional calculus. Physica A 389, 4613-4622 (2010)
    • (2010) Physica A , vol.389 , pp. 4613-4622
    • Herrmann, R.1
  • 6
    • 84867021459 scopus 로고    scopus 로고
    • On generalized fractional q-integral operators involving the q-gauss hypergeometric function
    • Purohit, SD, Yadav, RK: On generalized fractional q-integral operators involving the q-Gauss hypergeometric function. Bull. Math. Anal. Appl. 2, 35-44 (2010)
    • (2010) Bull. Math. Anal. Appl. , vol.2 , pp. 35-44
    • Purohit, S.D.1    Yadav, R.K.2
  • 7
    • 79958719410 scopus 로고    scopus 로고
    • Linear systems of fractional nabla difference equations
    • Atici, FM, Eloe, PW: Linear systems of fractional nabla difference equations. Rocky Mt. J. Math. 41, 353-370 (2011)
    • (2011) Rocky Mt. J. Math. , vol.41 , pp. 353-370
    • Atici, F.M.1    Eloe, P.W.2
  • 8
    • 84974177889 scopus 로고
    • Some fractional q-integrals and q-derivatives
    • Al-Salam, WA: Some fractional q-integrals and q-derivatives. Proc. Edinb. Math. Soc. 15, 135-140 (1966)
    • (1966) Proc. Edinb. Math. Soc. , vol.15 , pp. 135-140
    • Al-Salam, W.A.1
  • 9
    • 84971113538 scopus 로고
    • Certain fractional q-integrals and q-derivatives
    • Agarwal, R: Certain fractional q-integrals and q-derivatives. Proc. Camb. Philos. Soc. 66, 365-370 (1969)
    • (1969) Proc. Camb. Philos. Soc. , vol.66 , pp. 365-370
    • Agarwal, R.1
  • 10
    • 0008528081 scopus 로고
    • A fractional leibniz q-formula
    • Al-Salam, W, Verma, A: A fractional Leibniz q-formula. Pac. J. Math. 60, 1-9 (1975)
    • (1975) Pac. J. Math. , vol.60 , pp. 1-9
    • Al-Salam, W.1    Verma, A.2
  • 11
    • 79951617996 scopus 로고    scopus 로고
    • Observability of linear q-difference fractional-order systems with finite initial memory
    • Mozyrska, D, Pawluszewicz, E: Observability of linear q-difference fractional-order systems with finite initial memory. Bull. Pol. Acad. Sci. 58, 601-605 (2010)
    • (2010) Bull. Pol. Acad. Sci. , vol.58 , pp. 601-605
    • Mozyrska, D.1    Pawluszewicz, E.2
  • 12
    • 79960269969 scopus 로고    scopus 로고
    • Caputo q-fractional initial value problems and a q-analogue mittag-leffler function
    • Abdeljawad, T, Baleanu, D: Caputo q-fractional initial value problems and a q-analogue Mittag-Leffler function. Commun. Nonlinear Sci. Numer. Simul. 16, 4682-4688 (2011)
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 4682-4688
    • Abdeljawad, T.1    Baleanu, D.2
  • 13
    • 78651236363 scopus 로고    scopus 로고
    • Positive solutions for a class of boundary value problems with fractional q-differences
    • Ferreira, RAC: Positive solutions for a class of boundary value problems with fractional q-differences. Comput. Math. Appl. 61, 367-373 (2011)
    • (2011) Comput. Math. Appl. , vol.61 , pp. 367-373
    • Ferreira, R.A.C.1
  • 14
    • 84871300641 scopus 로고    scopus 로고
    • On nonlocal boundary value problems of nonlinear q-difference equations
    • Ahmad, B, Nieto, JJ: On nonlocal boundary value problems of nonlinear q-difference equations. Adv. Differ. Equ. 2012, 81 (2012)
    • (2012) Adv. Differ. Equ. , vol.2012 , pp. 81
    • Ahmad, B.1    Nieto, J.J.2
  • 15
    • 84873356580 scopus 로고    scopus 로고
    • Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations
    • Ahmad, B, Ntouyas, SK, Purnaras, IK: Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations. Adv. Differ. Equ. 2012, 140 (2012)
    • (2012) Adv. Differ. Equ. , vol.2012 , pp. 140
    • Ahmad, B.1    Ntouyas, S.K.2    Purnaras, I.K.3
  • 16
    • 84860430866 scopus 로고    scopus 로고
    • Positive solutions for a class of higher order boundary value problems with fractional q-derivatives
    • Graef, JR, Kong, L: Positive solutions for a class of higher order boundary value problems with fractional q-derivatives. Appl. Math. Comput. 218, 9682-9689 (2012)
    • (2012) Appl. Math. Comput. , vol.218 , pp. 9682-9689
    • Graef, J.R.1    Kong, L.2
  • 17
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He, JH: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Eng. 167, 57-68 (1998)
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.167 , pp. 57-68
    • He, J.H.1
  • 18
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method -A kind of non-Linear analytical technique: Some examples
    • He, JH: Variational iteration method - a kind of non-linear analytical technique: some examples. Int. J. Non-Linear Mech. 34, 699-708 (1999)
    • (1999) Int. J. Non-Linear Mech. , vol.34 , pp. 699-708
    • He, J.H.1
  • 19
    • 34250668369 scopus 로고    scopus 로고
    • Variational iteration method -some recent results and new interpretations
    • He, JH: Variational iteration method - some recent results and new interpretations. J. Comput. Appl. Math. 207, 3-17 (2007)
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 3-17
    • He, J.H.1
  • 20
    • 34748870677 scopus 로고    scopus 로고
    • Variational iteration method: New development and applications
    • He, JH, Wu, XH: Variational iteration method: new development and applications. Comput. Math. Appl. 54, 881-894 (2007)
    • (2007) Comput. Math. Appl. , vol.54 , pp. 881-894
    • He, J.H.1    Wu, X.H.2
  • 21
    • 4444374711 scopus 로고    scopus 로고
    • Solving riccati differential equation using adomian's decomposition method
    • El-Tawil, MA, Bahnasawi, AA, Abdel-Naby, A: Solving Riccati differential equation using Adomian's decomposition method. Appl. Math. Comput. 157, 503-514 (2004)
    • (2004) Appl. Math. Comput. , vol.157 , pp. 503-514
    • El-Tawil, M.A.1    Bahnasawi, A.A.2    Abdel-Naby, A.3
  • 22
    • 0015484437 scopus 로고
    • Comparing numerical methods for ordinary differential equations
    • Hull, T, Enright, W, Fellen, B, Sedgwick, A: Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9, 603-637 (1972)
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 603-637
    • Hull, T.1    Enright, W.2    Fellen, B.3    Sedgwick, A.4
  • 26
    • 0007190172 scopus 로고
    • Q-form of taylor's theorem
    • Jackson, FH: q-form of Taylor's theorem. Messenger Math. 38, 62-64 (1909)
    • (1909) Messenger Math. , vol.38 , pp. 62-64
    • Jackson, F.H.1
  • 27
  • 28
    • 84893948904 scopus 로고    scopus 로고
    • Variational iteration method for q-diffusion equations on time scales
    • in press
    • Wu, GC: Variational iteration method for q-diffusion equations on time scales. Heat Transf. Res. (2012, in press)
    • Heat Transf. Res. , vol.2012
    • Wu, G.C.1
  • 29
    • 84864939742 scopus 로고    scopus 로고
    • Variational iteration method for q-difference equations of second order
    • Wu, GC: Variational iteration method for q-difference equations of second order. J. Appl. Math. 2012, 102850 (2012)
    • (2012) J. Appl. Math. , vol.2012 , pp. 102850
    • Wu, G.C.1
  • 30
    • 84870901403 scopus 로고    scopus 로고
    • Lagrange multipliers of q-difference equations of third order
    • Kong, H, Huang, LL: Lagrange multipliers of q-difference equations of third order. Commun. Fract. Calc. 3, 30-33 (2012)
    • (2012) Commun. Fract. Calc. , vol.3 , pp. 30-33
    • Kong, H.1    Huang, L.L.2
  • 31
  • 33
    • 79251595176 scopus 로고    scopus 로고
    • Application of numerical inverse laplace transform algorithms in fractional calculus
    • Sheng, H, Li, Y, Chen, YQ: Application of numerical inverse Laplace transform algorithms in fractional calculus. J. Franklin Inst. 348, 315-330 (2011)
    • (2011) J. Franklin Inst. , vol.348 , pp. 315-330
    • Sheng, H.1    Li, Y.2    Chen, Y.Q.3
  • 34
    • 84870873877 scopus 로고    scopus 로고
    • Variational iteration method for the fractional diffusion equations in porous media
    • Wu, GC: Variational iteration method for the fractional diffusion equations in porous media. Chin. Phys. B 21, 120504 (2012)
    • (2012) Chin. Phys. , vol.B 21 , pp. 120504
    • Wu, G.C.1
  • 35
    • 84875378030 scopus 로고    scopus 로고
    • Variational iteration method for the burgers' flow with fractional derivatives -new lagrange multipliers
    • in press, doi:10.1016/j.apm.2012.12.018
    • Wu, GC, Baleanu, D: Variational iteration method for the Burgers' flow with fractional derivatives - new Lagrange multipliers. Appl. Math. Model. (2012, in press). doi:10.1016/j.apm.2012.12.018
    • Appl. Math. Model. , vol.2012
    • Wu, G.C.1    Baleanu, D.2
  • 36
    • 76549123950 scopus 로고    scopus 로고
    • Solving of the nonlinear and linear schrödinger equations by the homotopy perturbation method
    • Baleanu, D, Golmankhaneh, AK, Golmankhaneh, AK: Solving of the nonlinear and linear Schrödinger equations by the homotopy perturbation method. Rom. J. Phys. 54, 823-832 (2010)
    • (2010) Rom. J. Phys. , vol.54 , pp. 823-832
    • Baleanu, D.1    Golmankhaneh, A.K.2    Golmankhaneh, A.K.3
  • 38
    • 35748962937 scopus 로고    scopus 로고
    • Fractional q-calculus on a time scale
    • Atici, FM, Eloe, PW: Fractional q-calculus on a time scale. J. Nonlinear Math. Phys. 14, 341-352 (2007)
    • (2007) J. Nonlinear Math. Phys. , vol.14 , pp. 341-352
    • Atici, F.M.1    Eloe, P.W.2
  • 39
    • 0000243146 scopus 로고
    • Beiträge zur theorie der heineschen reihen
    • Die 24 Integrale der hypergeometrischen q-Differenzengleichung. Das q-Analogon der Laplace-Transformation
    • Hahn, W: Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q-Differenzengleichung. Das q-Analogon der Laplace-Transformation. Math. Nachr. 2, 340-379 (1949)
    • (1949) Math. Nachr. , vol.2 , pp. 340-379
    • Hahn, W.1
  • 41
    • 78751639434 scopus 로고    scopus 로고
    • The exact solutions of fuzzy wave-like equations with variable coefficients by a variational iteration method
    • Allahviranloo, T, Abbasbandy, S, Rouhparvar, H: The exact solutions of fuzzy wave-like equations with variable coefficients by a variational iteration method. Appl. Soft Comput. 11, 2186-2192 (2011)
    • (2011) Appl. Soft Comput. , vol.11 , pp. 2186-2192
    • Allahviranloo, T.1    Abbasbandy, S.2    Rouhparvar, H.3
  • 42
    • 82555187128 scopus 로고    scopus 로고
    • The variational iteration method for solving n-th order fuzzy differential equation
    • Jafari, H, Saeidy, M, Baleanu, D: The variational iteration method for solving n-th order fuzzy differential equation. Cent. Eur. J. Phys. 10, 76-85 (2012)
    • (2012) Cent. Eur. J. Phys. , vol.10 , pp. 76-85
    • Jafari, H.1    Saeidy, M.2    Baleanu, D.3
  • 43
    • 84870941648 scopus 로고    scopus 로고
    • Homotopy perturbation and variational iteration methods for solving fuzzy differential equations
    • Jafari, H, Khalique, CM: Homotopy perturbation and variational iteration methods for solving fuzzy differential equations. Commun. Fract. Calc. 3, 38-48 (2012)
    • (2012) Commun. Fract. Calc. , vol.3 , pp. 38-48
    • Jafari, H.1    Khalique, C.M.2
  • 46
    • 80052684335 scopus 로고    scopus 로고
    • Variational optimal-control problems with delayed arguments on time scales
    • Abdeljawad, T, Jarad, F, Baleanu, D: Variational optimal-control problems with delayed arguments on time scales. Adv. Differ. Equ. 2009, 840386 (2009)
    • (2009) Adv. Differ. Equ. , vol.2009 , pp. 840386
    • Abdeljawad, T.1    Jarad, F.2    Baleanu, D.3
  • 51
    • 84874054174 scopus 로고    scopus 로고
    • A review of the adomian decomposition method and its applications to fractional differential equations
    • Duan, JS, Buleanu, D, Wazwaz, AM: A review of the Adomian decomposition method and its applications to fractional differential equations. Commun. Fract. Calc. 3, 73-99 (2012)
    • (2012) Commun. Fract. Calc. , vol.3 , pp. 73-99
    • Duan, J.S.1    Buleanu, D.2    Wazwaz, A.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.