메뉴 건너뛰기




Volumn , Issue , 2013, Pages

Spectral-collocation methods for fractional pantograph delay- integrodifferential equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84890023932     PISSN: 16879120     EISSN: 16879139     Source Type: Journal    
DOI: 10.1155/2013/821327     Document Type: Article
Times cited : (67)

References (35)
  • 2
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and therir approximations
    • He J. H., Some applications of nonlinear fractional differential equations and therir approximations. Bulletin of Science, Technology and Society 1999 15 86 90
    • (1999) Bulletin of Science, Technology and Society , vol.15 , pp. 86-90
    • He, J.H.1
  • 5
    • 33947164737 scopus 로고    scopus 로고
    • Fractional-order dynamical models of love
    • DOI 10.1016/j.chaos.2006.01.098, PII S0960077906001652
    • Ahmad W. M., El-Khazali R., Fractional-order dynamical models of love. Chaos, Solitons and Fractals 2007 33 4 1367 1375 10.1016/j.chaos.2006.01.098 MR2318922 ZBL1133.91539 (Pubitemid 46413017)
    • (2007) Chaos, Solitons and Fractals , vol.33 , Issue.4 , pp. 1367-1375
    • Ahmad, W.M.1    El-Khazali, R.2
  • 6
    • 33747286487 scopus 로고    scopus 로고
    • The time fractional diffusion equation and the advection-dispersion equation
    • Huang F., Liu F., The time fractional diffusion equation and the advection-dispersion equation. The ANZIAM Journal 2005 46 3 317 330 10.1017/S1446181100008282 MR2124926 ZBL1072.35218 (Pubitemid 44238538)
    • (2005) ANZIAM Journal , vol.46 , Issue.3 , pp. 317-330
    • Huang, F.1    Liu, F.2
  • 8
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • DOI 10.1016/S0096-3003(01)00167-9, PII S0096300301001679
    • Shawagfeh N. T., Analytical approximate solutions for nonlinear fractional differential equations. Applied Mathematics and Computation 2002 131 2-3 517 529 10.1016/S0096-3003(01)00167-9 MR1920243 ZBL1029.34003 (Pubitemid 34813503)
    • (2002) Applied Mathematics and Computation , vol.131 , Issue.2-3 , pp. 517-529
    • Shawagfeh, N.T.1
  • 11
    • 84857583048 scopus 로고    scopus 로고
    • The approximate and exact solutions of the fractional-order delay differential equations using Legendre seudospectral method
    • 2-s2.0-84857583048
    • Khader M. M., Hendy A. S., The approximate and exact solutions of the fractional-order delay differential equations using Legendre seudospectral method. International Journal of Pure and Applied Mathematics 2012 74 3 287 297 2-s2.0-84857583048
    • (2012) International Journal of Pure and Applied Mathematics , vol.74 , Issue.3 , pp. 287-297
    • Khader, M.M.1    Hendy, A.S.2
  • 12
    • 80155210277 scopus 로고    scopus 로고
    • A Legendre collocation method for fractional integro-differential equations
    • 10.1177/1077546310395977 MR2895862 ZBL06205953
    • Saadatmandi A., Dehghan M., A Legendre collocation method for fractional integro-differential equations. Journal of Vibration and Control 2011 17 13 2050 2058 10.1177/1077546310395977 MR2895862 ZBL06205953
    • (2011) Journal of Vibration and Control , vol.17 , Issue.13 , pp. 2050-2058
    • Saadatmandi, A.1    Dehghan, M.2
  • 13
    • 80855129436 scopus 로고    scopus 로고
    • Legendre wavelets method for fractional integro-differential equations
    • MR2837704 ZBL1250.65160
    • Rawashdeh E. A., Legendre wavelets method for fractional integro-differential equations. Applied Mathematical Sciences 2011 5 2 2467 2474 MR2837704 ZBL1250.65160
    • (2011) Applied Mathematical Sciences , vol.5 , Issue.2 , pp. 2467-2474
    • Rawashdeh, E.A.1
  • 14
    • 79957889333 scopus 로고    scopus 로고
    • The Legendre wavelet method for solving fractional differential equations
    • 10.1016/j.cnsns.2011.01.014 MR2806727 ZBL1222.65063
    • Rehman M., Khan R. A., 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 MR2806727 ZBL1222.65063
    • (2011) Communications in Nonlinear Science and Numerical Simulation , vol.16 , Issue.11 , pp. 4163-4173
    • Rehman, M.1    Khan, R.A.2
  • 15
    • 84866686370 scopus 로고    scopus 로고
    • A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals
    • 10.1186/1687-2770-2012-62 MR3085724
    • Bhrawy A. H., Alghamdi M. A., A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals. Boundary Value Problems 2012 1 62 1 13 10.1186/1687-2770-2012-62 MR3085724
    • (2012) Boundary Value Problems , vol.1 , Issue.62 , pp. 1-13
    • Bhrawy, A.H.1    Alghamdi, M.A.2
  • 16
    • 79960555480 scopus 로고    scopus 로고
    • Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
    • 10.1016/j.apm.2011.05.011 MR2820942 ZBL1228.65126
    • Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Applied Mathematical Modelling 2011 35 12 5662 5672 10.1016/j.apm.2011.05.011 MR2820942 ZBL1228.65126
    • (2011) Applied Mathematical Modelling , vol.35 , Issue.12 , pp. 5662-5672
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 17
    • 80052270048 scopus 로고    scopus 로고
    • A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
    • 10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
    • Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Computers & Mathematics with Applications 2011 62 5 2364 2373 10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.5 , pp. 2364-2373
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 18
    • 79960376707 scopus 로고    scopus 로고
    • A Chebyshev pseudo-spectral method for solving fractional-order integro-differential equations
    • 10.1017/S1446181110000830 MR2780994 ZBL1216.65187
    • Sweilam N. H., Khader M. M., A Chebyshev pseudo-spectral method for solving fractional-order integro-differential equations. The ANZIAM Journal 2010 51 4 464 475 10.1017/S1446181110000830 MR2780994 ZBL1216.65187
    • (2010) The ANZIAM Journal , vol.51 , Issue.4 , pp. 464-475
    • Sweilam, N.H.1    Khader, M.M.2
  • 19
    • 79961168894 scopus 로고    scopus 로고
    • A quadrature tau method for fractional differential equations with variable coefficients
    • 10.1016/j.aml.2011.06.016 MR2826154 ZBL1269.65068
    • Bhrawy A. H., Alofi A. S., Ezz-Eldien S. S., A quadrature tau method for fractional differential equations with variable coefficients. Applied Mathematics Letters 2011 24 12 2146 2152 10.1016/j.aml.2011.06.016 MR2826154 ZBL1269.65068
    • (2011) Applied Mathematics Letters , vol.24 , Issue.12 , pp. 2146-2152
    • Bhrawy, A.H.1    Alofi, A.S.2    Ezz-Eldien, S.S.3
  • 20
    • 84864987975 scopus 로고    scopus 로고
    • A shifted Legendre spectral method for fractional-order multi-point boundary value problems
    • 10.1186/1687-1847-2012-8
    • Bhrawy A. H., Alshomrani M., A shifted Legendre spectral method for fractional-order multi-point boundary value problems. Advances in Difference Equations 2012 2012, article 8 10.1186/1687-1847-2012-8
    • (2012) Advances in Difference Equations , pp. 20128
    • Bhrawy, A.H.1    Alshomrani, M.2
  • 21
    • 74249095517 scopus 로고    scopus 로고
    • A new operational matrix for solving fractional-order differential equations
    • 10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
    • Saadatmandi A., Dehghan M., A new operational matrix for solving fractional-order differential equations. Computers & Mathematics with Applications 2010 59 3 1326 1336 10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.3 , pp. 1326-1336
    • Saadatmandi, A.1    Dehghan, M.2
  • 22
    • 84872609098 scopus 로고    scopus 로고
    • A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations
    • 10.1016/j.apm.2012.08.022 MR3020568 ZBL06198514
    • Bhrawy A. H., Tharwat M. M., Yildirim A., A new formula for fractional integrals of Chebyshev polynomials: application for solving multi-term fractional differential equations. Applied Mathematical Modelling 2013 37 6 4245 4252 10.1016/j.apm.2012.08.022 MR3020568 ZBL06198514
    • (2013) Applied Mathematical Modelling , vol.37 , Issue.6 , pp. 4245-4252
    • Bhrawy, A.H.1    Tharwat, M.M.2    Yildirim, A.3
  • 23
    • 84866046515 scopus 로고    scopus 로고
    • The operational matrix of fractional integration for shifted Chebyshev polynomials
    • 10.1016/j.aml.2012.01.027 MR2971394 ZBL1255.65147
    • Bhrawy A. H., Alofi A. S., The operational matrix of fractional integration for shifted Chebyshev polynomials. Applied Mathematics Letters 2013 26 1 25 31 10.1016/j.aml.2012.01.027 MR2971394 ZBL1255.65147
    • (2013) Applied Mathematics Letters , vol.26 , Issue.1 , pp. 25-31
    • Bhrawy, A.H.1    Alofi, A.S.2
  • 24
    • 84861893481 scopus 로고    scopus 로고
    • A new Jacobi operational matrix: An application for solving fractional differential equations
    • 10.1016/j.apm.2011.12.031 MR2930392 ZBL1252.34019
    • 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 10.1016/j.apm.2011.12.031 MR2930392 ZBL1252.34019
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.10 , pp. 4931-4943
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 25
    • 77952816520 scopus 로고    scopus 로고
    • Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
    • 10.1090/S0025-5718-09-02269-8 MR2552221 ZBL1207.65157
    • Chen Y., Tang T., Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel. Mathematics of Computation 2010 79 269 147 167 10.1090/S0025-5718-09-02269-8 MR2552221 ZBL1207.65157
    • (2010) Mathematics of Computation , vol.79 , Issue.269 , pp. 147-167
    • Chen, Y.1    Tang, T.2
  • 26
    • 84862506497 scopus 로고    scopus 로고
    • Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions
    • MR2876648 ZBL1262.45005
    • Wei Y., Chen Y., Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions. Advances in Applied Mathematics and Mechanics 2012 4 1 1 20 MR2876648 ZBL1262.45005
    • (2012) Advances in Applied Mathematics and Mechanics , vol.4 , Issue.1 , pp. 1-20
    • Wei, Y.1    Chen, Y.2
  • 28
    • 0035449760 scopus 로고    scopus 로고
    • Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey
    • DOI 10.1016/S0377-0427(00)00557-4, PII S0377042700005574
    • Mastroianni G., Occorsio D., Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey. Journal of Computational and Applied Mathematics 2001 134 1-2 325 341 10.1016/S0377-0427(00)00557-4 MR1852573 ZBL0990.41003 (Pubitemid 32836233)
    • (2001) Journal of Computational and Applied Mathematics , vol.134 , Issue.1-2 , pp. 325-341
    • Mastroianni, G.1    Occorsio, D.2
  • 30
    • 84966237716 scopus 로고
    • Polynomial approximation on compact manifolds and homogeneous spaces
    • MR0410210 10.1090/S0002-9947-1970-0410210-0 ZBL0208.14701
    • Ragozin D. L., Polynomial approximation on compact manifolds and homogeneous spaces. Transactions of the American Mathematical Society 1970 150 41 53 MR0410210 10.1090/S0002-9947-1970-0410210-0 ZBL0208.14701
    • (1970) Transactions of the American Mathematical Society , vol.150 , pp. 41-53
    • Ragozin, D.L.1
  • 31
    • 0000071649 scopus 로고
    • Constructive polynomial approximation on spheres and projective spaces
    • MR0288468
    • Ragozin D. L., Constructive polynomial approximation on spheres and projective spaces. Transactions of the American Mathematical Society 1971 162 157 170 MR0288468
    • (1971) Transactions of the American Mathematical Society , vol.162 , pp. 157-170
    • Ragozin, D.L.1
  • 33
    • 0000762664 scopus 로고
    • Mean convergence of Lagrange interpolation. III
    • 10.2307/1999259 MR732113 ZBL0577.41001
    • Nevai P., Mean convergence of Lagrange interpolation. III. Transactions of the American Mathematical Society 1984 282 2 669 698 10.2307/1999259 MR732113 ZBL0577.41001
    • (1984) Transactions of the American Mathematical Society , vol.282 , Issue.2 , pp. 669-698
    • Nevai, P.1
  • 35
    • 84880177806 scopus 로고    scopus 로고
    • Two efficient generalized Laguerre spectral algorithms for fractional initial value problems
    • 546502 MR3066294 10.1155/2013/546502
    • Baleanu D., Bhrawy A. H., Taha T. M., Two efficient generalized Laguerre spectral algorithms for fractional initial value problems. Abstract and Applied Analysis 2013 2013 10 546502 MR3066294 10.1155/2013/546502
    • (2013) Abstract and Applied Analysis , vol.2013 , pp. 10
    • Baleanu, D.1    Bhrawy, A.H.2    Taha, T.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.