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Volumn 2012, Issue , 2012, Pages

An adaptive pseudospectral method for fractional order boundary value problems

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EID: 84872169204     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2012/381708     Document Type: Article
Times cited : (21)

References (28)
  • 1
    • 65049084831 scopus 로고    scopus 로고
    • Hackensack, NJ, USA World Scientific Publishing Series on Complexity, Nonlinearity and Chaos 10.1142/9789814355216 2894576 ZBL1244.49028
    • Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fractional Calculus: Models and Numerical Methods 2012 3 Hackensack, NJ, USA World Scientific Publishing Series on Complexity, Nonlinearity and Chaos 10.1142/9789814355216 2894576 ZBL1244.49028
    • (2012) Fractional Calculus: Models and Numerical Methods , vol.3
    • Baleanu, D.1    Diethelm, K.2    Scalas, E.3    Trujillo, J.J.4
  • 2
    • 0003797958 scopus 로고    scopus 로고
    • San Diego, Calif, USA Academic Press 1658022 ZBL1056.93542
    • Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press 1658022 ZBL1056.93542
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 4
    • 79961000780 scopus 로고    scopus 로고
    • Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems
    • 10.1016/j.camwa.2011.03.059 2824694 ZBL1228.65119
    • Moaddy K., Hashim I., Momani S., Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. Computers & Mathematics with Applications 2011 62 3 1068 1074 10.1016/j.camwa.2011.03.059 2824694 ZBL1228.65119
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.3 , pp. 1068-1074
    • Moaddy, K.1    Hashim, I.2    Momani, S.3
  • 5
    • 84859537689 scopus 로고    scopus 로고
    • Piecewise polynomial collocation for linear boundary value problems of fractional differential equations
    • 10.1016/j.cam.2012.03.002 2912696
    • Pedas A., Tamme E., Piecewise polynomial collocation for linear boundary value problems of fractional differential equations. Journal of Computational and Applied Mathematics 2012 236 13 3349 3359 10.1016/j.cam.2012.03.002 2912696
    • (2012) Journal of Computational and Applied Mathematics , vol.236 , Issue.13 , pp. 3349-3359
    • Pedas, A.1    Tamme, E.2
  • 6
    • 77952705214 scopus 로고    scopus 로고
    • A collocation-shooting method for solving fractional boundary value problems
    • 10.1016/j.cnsns.2010.01.020 2652654 ZBL1222.65078
    • Al-Mdallal Q. M., Syam M. I., Anwar M. N., A collocation-shooting method for solving fractional boundary value problems. Communications in Nonlinear Science and Numerical Simulation 2010 15 12 3814 3822 10.1016/j.cnsns.2010.01. 020 2652654 ZBL1222.65078
    • (2010) Communications in Nonlinear Science and Numerical Simulation , vol.15 , Issue.12 , pp. 3814-3822
    • Al-Mdallal, Q.M.1    Syam, M.I.2    Anwar, M.N.3
  • 7
    • 67349259080 scopus 로고    scopus 로고
    • Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations
    • 10.1016/j.cam.2008.04.003 2527892 ZBL1166.65066
    • Ford N. J., Connolly J. A., Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations. Journal of Computational and Applied Mathematics 2009 229 2 382 391 10.1016/j.cam.2008.04. 003 2527892 ZBL1166.65066
    • (2009) Journal of Computational and Applied Mathematics , vol.229 , Issue.2 , pp. 382-391
    • Ford, N.J.1    Connolly, J.A.2
  • 8
    • 33744981446 scopus 로고    scopus 로고
    • Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method
    • DOI 10.1016/j.amc.2005.11.025, PII S0096300305009276
    • Momani S., Odibat Z., Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method. Applied Mathematics and Computation 2006 177 2 488 494 10.1016/j.amc.2005.11.025 2291973 ZBL1096.65131 (Pubitemid 43866876)
    • (2006) Applied Mathematics and Computation , vol.177 , Issue.2 , pp. 488-494
    • Momani, S.1    Odibat, Z.2
  • 9
    • 77953478991 scopus 로고    scopus 로고
    • Fractional variational iteration method and its application
    • 10.1016/j.physleta.2010.04.034 2640023 ZBL1237.34007
    • Wu G., Lee E. W. M., Fractional variational iteration method and its application. Physics Letters A 2010 374 25 2506 2509 10.1016/j.physleta.2010.04. 034 2640023 ZBL1237.34007
    • (2010) Physics Letters A , vol.374 , Issue.25 , pp. 2506-2509
    • Wu, G.1    Lee, E.W.M.2
  • 10
    • 34250647432 scopus 로고    scopus 로고
    • An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method
    • DOI 10.1016/j.cam.2006.07.011, PII S0377042706004602, Variational Iteration Method-Reality, Potential, and Challenges
    • Abbasbandy S., An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method. Journal of Computational and Applied Mathematics 2007 207 1 53 58 10.1016/j.cam.2006.07.011 2332946 ZBL1120.65133 (Pubitemid 46935385)
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , Issue.1 , pp. 53-58
    • Abbasbandy, S.1
  • 11
    • 84860388823 scopus 로고    scopus 로고
    • A short remark on fractional variational iteration method
    • 10.1016/j.physleta.2011.07.033 2826245
    • He J.-H., A short remark on fractional variational iteration method. Physics Letters A 2011 375 38 3362 3364 10.1016/j.physleta.2011.07.033 2826245
    • (2011) Physics Letters A , vol.375 , Issue.38 , pp. 3362-3364
    • He, J.-H.1
  • 12
    • 74449084990 scopus 로고    scopus 로고
    • The variational iteration method which should be followed
    • He J. H., Wu G. C., Austin F., The variational iteration method which should be followed. Nonlinear Science Letters A 2010 1 1 1 30
    • (2010) Nonlinear Science Letters A , vol.1 , Issue.1 , pp. 1-30
    • He, J.H.1    Wu, G.C.2    Austin, F.3
  • 13
    • 80053385266 scopus 로고    scopus 로고
    • The construction of operational matrix of fractional derivatives using B-spline functions
    • 10.1016/j.cnsns.2011.07.018 2843781
    • Lakestani M., Dehghan M., Irandoust-pakchin S., The construction of operational matrix of fractional derivatives using B-spline functions. Communications in Nonlinear Science and Numerical Simulation 2012 17 3 1149 1162 10.1016/j.cnsns.2011.07.018 2843781
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.3 , pp. 1149-1162
    • Lakestani, M.1    Dehghan, M.2    Irandoust-Pakchin, S.3
  • 14
    • 83655192025 scopus 로고    scopus 로고
    • A numerical method for solving boundary value problems for fractional differential equations
    • 10.1016/j.apm.2011.07.045 2872865 ZBL1243.65095
    • Rehman M. U., Khan R. A., A numerical method for solving boundary value problems for fractional differential equations. Applied Mathematical Modelling 2012 36 3 894 907 10.1016/j.apm.2011.07.045 2872865 ZBL1243.65095
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.3 , pp. 894-907
    • Rehman, M.U.1    Khan, R.A.2
  • 15
    • 84861893481 scopus 로고    scopus 로고
    • A new Jacobi operational matrix: An application for solving fractional differential equations
    • Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A new Jacobi operational matrix: an application for solving fractional differential equations. Applied Mathematical Modelling 2012 36 10 4931 4943
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.10 , pp. 4931-4943
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 16
    • 79957889333 scopus 로고    scopus 로고
    • The Legendre wavelet method for solving fractional differential equations
    • 10.1016/j.cnsns.2011.01.014 2806727 ZBL1222.65063
    • Rehman M. U., Ali Khan R., The Legendre wavelet method for solving fractional differential equations. Communications in Nonlinear Science and Numerical Simulation 2011 16 11 4163 4173 10.1016/j.cnsns.2011.01.014 2806727 ZBL1222.65063
    • (2011) Communications in Nonlinear Science and Numerical Simulation , vol.16 , Issue.11 , pp. 4163-4173
    • Rehman, M.U.1    Ali Khan, R.2
  • 17
    • 41949112904 scopus 로고    scopus 로고
    • Application of homotopy-perturbation method to fractional IVPs
    • DOI 10.1016/j.cam.2007.06.010, PII S0377042707003081
    • Abdulaziz O., Hashim I., Momani S., Application of homotopy-perturbation method to fractional IVPs. Journal of Computational and Applied Mathematics 2008 216 2 574 584 10.1016/j.cam.2007.06.010 2412931 ZBL1142.65104 (Pubitemid 351509724)
    • (2008) Journal of Computational and Applied Mathematics , vol.216 , Issue.2 , pp. 574-584
    • Abdulaziz, O.1    Hashim, I.2    Momani, S.3
  • 19
    • 84859716386 scopus 로고    scopus 로고
    • Solving linear and nonlinear fractional differential equations using spline functions
    • 426514 10.1016/j.amc.2012.07.047
    • Al-Rabtah A., Momani S., Ramadan M. A., Solving linear and nonlinear fractional differential equations using spline functions. Abstract and Applied Analysis 2012 2012 9 426514 10.1016/j.amc.2012.07.047
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 9
    • Al-Rabtah, A.1    Momani, S.2    Ramadan, M.A.3
  • 20
    • 84863687996 scopus 로고    scopus 로고
    • Positive solutions of an initial value problem for nonlinear fractional differential equations
    • 837437 10.1155/2012/837437
    • Baleanu D., Mohammadi H., Rezapour S., Positive solutions of an initial value problem for nonlinear fractional differential equations. Abstract and Applied Analysis 2012 2012 7 837437 10.1155/2012/837437
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 7
    • Baleanu, D.1    Mohammadi, H.2    Rezapour, S.3
  • 21
    • 84855203771 scopus 로고    scopus 로고
    • Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus
    • 10.1016/j.physleta.2011.11.030 2877722
    • He J.-H., Elagan S. K., Li Z. B., Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus. Physics Letters A 2012 376 4 257 259 10.1016/j.physleta.2011.11.030 2877722
    • (2012) Physics Letters A , vol.376 , Issue.4 , pp. 257-259
    • He, J.-H.1    Elagan, S.K.2    Li, Z.B.3
  • 22
    • 0032136257 scopus 로고    scopus 로고
    • Physical and geometrical interpretation of fractional operators
    • PII S0016003297000483
    • Moshrefi-Torbati M., Hammond J. K., Physical and geometrical interpretation of fractional operators. Journal of the Franklin Institute B 1998 335 6 1077 1086 10.1016/S0016-0032(97)00048-3 1625806 ZBL0989.26004 (Pubitemid 128389676)
    • (1998) Journal of the Franklin Institute , vol.335 , Issue.6 , pp. 1077-1086
    • Moshrefi-Torbati, M.1    Hammond, J.K.2
  • 23
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • Caputo M., Linear models of dissipation whose Q is almost frequency independent. Journal of the Royal Australian Society 1967 13, Part 2 529 539
    • (1967) Journal of the Royal Australian Society , vol.132 , pp. 529-539
    • Caputo, M.1
  • 25
    • 84867583222 scopus 로고    scopus 로고
    • Solution of time-varying delay systems using an adaptive collocation method
    • Maleki M., Hashim I., Abbasbandy S., Solution of time-varying delay systems using an adaptive collocation method. Applied Mathematics and Computation 2012 219 4 1434 1448
    • (2012) Applied Mathematics and Computation , vol.219 , Issue.4 , pp. 1434-1448
    • Maleki, M.1    Hashim, I.2    Abbasbandy, S.3
  • 26
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Torvik P. J., Bagley R. L., On the appearance of the fractional derivative in the behavior of real materials. Journal of Applied Mechanics 1984 51 2 294 298 2-s2.0-0021439912 10.1115/1.3167615 ZBL1203.74022 (Pubitemid 14583152)
    • (1984) Journal of Applied Mechanics, Transactions ASME , vol.51 , Issue.2 , pp. 294-298
    • Torvik, P.J.1    Bagley, R.L.2
  • 27
    • 75149147525 scopus 로고    scopus 로고
    • The solution of the Bagley-Torvik equation with the generalized Taylor collocation method
    • 10.1016/j.jfranklin.2009.10.007 2593729 ZBL1188.65107
    • Çenesiz Y., Keskin Y., Kurnaz A., The solution of the Bagley-Torvik equation with the generalized Taylor collocation method. Journal of the Franklin Institute 2010 347 2 452 466 10.1016/j.jfranklin.2009.10.007 2593729 ZBL1188.65107
    • (2010) Journal of the Franklin Institute , vol.347 , Issue.2 , pp. 452-466
    • Çenesiz, Y.1    Keskin, Y.2    Kurnaz, A.3
  • 28
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • DOI 10.1016/j.chaos.2005.10.068, PII S0960077905010374
    • Momani S., Odibat Z., Numerical comparison of methods for solving linear differential equations of fractional order. Chaos, Solitons & Fractals 2007 31 5 1248 1255 10.1016/j.chaos.2005.10.068 2262130 ZBL1137.65450 (Pubitemid 44345225)
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.5 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2


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