메뉴 건너뛰기




Volumn 2012, Issue , 2012, Pages

A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals

Author keywords

Collocation method; Fractional Langevin equation; Jacobi Gauss Lobatto quadrature; Shifted Jacobi polynomials; Three point boundary conditions

Indexed keywords


EID: 84866686370     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1186/1687-2770-2012-62     Document Type: Article
Times cited : (73)

References (36)
  • 4
    • 84866046515 scopus 로고    scopus 로고
    • The operational matrix of fractional integration for shifted chebyshev polynomials
    • doi:10.1016/j.aml.2012.01.027
    • Bhrawy, AH, Alofi, AS: The operational matrix of fractional integration for shifted Chebyshev polynomials. Appl. Math. Lett. (2012). doi:10.1016/j.aml.2012.01.027
    • (2012) Appl. Math. Lett.
    • Bhrawy, A.H.1    Alofi, A.S.2
  • 5
    • 79960999102 scopus 로고    scopus 로고
    • A numerical technique for solving fractional optimal control problems
    • Lotfi, A, Dehghan, M, Yousefi, SA: A numerical technique for solving fractional optimal control problems. Comput. Math. Appl. 62, 1055-1067 (2011)
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1055-1067
    • Lotfi, A.1    Dehghan, M.2    Yousefi, S.A.3
  • 6
    • 80053385266 scopus 로고    scopus 로고
    • The construction of operational matrix of fractional derivatives using B-spline functions
    • Lakestani, M, Dehghan, M, Irandoust-pakchin, S: The construction of operational matrix of fractional derivatives using B-spline functions. Commun. Nonlinear Sci. Numer. Simul. 17, 1149-1162 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 1149-1162
    • Lakestani, M.1    Dehghan, M.2    Irandoust-Pakchin, S.3
  • 7
    • 84859537689 scopus 로고    scopus 로고
    • Piecewise polynomial collocation for linear boundary value problems of fractional differential equations
    • doi:10.1016/j.cam.2012.03.002
    • Pedas, A, Tamme, E: Piecewise polynomial collocation for linear boundary value problems of fractional differential equations. J. Comput. Appl. Math. (2012). doi:10.1016/j.cam.2012.03.002
    • (2012) J. Comput. Appl. Math.
    • Pedas, A.1    Tamme, E.2
  • 8
    • 79961168894 scopus 로고    scopus 로고
    • A quadrature tau method for variable coefficients fractional differential equations
    • Bhrawy, AH, Alofi, AS, Ezz-Eldien, SS: A quadrature tau method for variable coefficients fractional differential equations. Appl. Math. Lett. 24, 2146-2152 (2011)
    • (2011) Appl. Math. Lett. , vol.24 , pp. 2146-2152
    • Bhrawy, A.H.1    Alofi, A.S.2    Ezz-Eldien, S.S.3
  • 9
    • 84864987975 scopus 로고    scopus 로고
    • A shifted legendre spectral method for fractional-order multi-point boundary value problems
    • Bhrawy, AH, Alshomrani, M: A shifted Legendre spectral method for fractional-order multi-point boundary value problems. Adv. Differ. Equ. 2012, 8 (2012)
    • (2012) Adv. Differ. Equ. , vol.2012 , pp. 8
    • Bhrawy, A.H.1    Alshomrani, M.2
  • 10
    • 79960555480 scopus 로고    scopus 로고
    • Efficient chebyshev spectral methods for solving multi-term fractional orders differential equations
    • Doha, EH, Bhrawy, AH, Ezz-Eldien, SS: Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Appl. Math. Model. 35, 5662-5672 (2011)
    • (2011) Appl. Math. Model. , vol.35 , pp. 5662-5672
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 11
    • 80052270048 scopus 로고    scopus 로고
    • A chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
    • Doha, EH, Bhrawy, AH, Ezz-Eldien, SS: A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl. 62, 2364-2373 (2011)
    • (2011) Comput. Math. Appl. , vol.62 , pp. 2364-2373
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3
  • 12
    • 80054946851 scopus 로고    scopus 로고
    • A study of nonlinear langevin equation involving two fractional orders in different intervals
    • Ahmad, B, Nieto, JJ, Alsaedi, A, El-Shahed, M: A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal., Real World Appl. 13, 599-606 (2012)
    • (2012) Nonlinear Anal., Real World Appl. , vol.13 , pp. 599-606
    • Ahmad, B.1    Nieto, J.J.2    Alsaedi, A.3    El-Shahed, M.4
  • 13
    • 77956906008 scopus 로고    scopus 로고
    • Solvability of nonlinear langevin equation involving two fractional orders with dirichlet boundary conditions
    • Article ID 649486 doi:10.1155/2010/649486
    • Ahmad, B, Nieto, JJ: Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions. Int. J. Differ. Equ. 2010, Article ID 649486 (2010). doi:10.1155/2010/649486
    • (2010) Int. J. Differ. Equ. , vol.2010
    • Ahmad, B.1    Nieto, J.J.2
  • 14
    • 79959261387 scopus 로고    scopus 로고
    • Existence of solutions to nonlinear langevin equation involving two fractional orders with boundary value conditions
    • Article ID 516481 doi:10.1155/2011/516481
    • Chen, A, Chen, Y: Existence of solutions to nonlinear Langevin equation involving two fractional orders with boundary value conditions. Bound. Value Probl. 2011, Article ID 516481 (2011). doi:10.1155/2011/516481
    • (2011) Bound. Value Probl. , vol.2011
    • Chen, A.1    Chen, Y.2
  • 15
    • 36749074902 scopus 로고    scopus 로고
    • Fractional Langevin equation and Riemann-Liouville fractional derivative
    • DOI 10.1140/epje/i2007-10224-2
    • Fa, KS: Fractional Langevin equation and Riemann-Liouville fractional derivative. Eur. Phys. J. E 24, 139-143 (2007) (Pubitemid 350212092)
    • (2007) European Physical Journal E , vol.24 , Issue.2 , pp. 139-143
    • Fa, K.S.1
  • 16
    • 45849155458 scopus 로고    scopus 로고
    • Fractional langevin model of memory in financial markets
    • Picozzi, S, West, B: Fractional Langevin model of memory in financial markets. Phys. Rev. E 66, 46-118 (2002)
    • (2002) Phys. Rev. E , vol.66 , pp. 46-118
    • Picozzi, S.1    West, B.2
  • 17
    • 52349118652 scopus 로고    scopus 로고
    • Langevin equation with two fractional orders
    • Lim, SC, Li, M, Teo, LP: Langevin equation with two fractional orders. Phys. Lett. A 372, 6309-6320 (2008)
    • (2008) Phys. Lett. A , vol.372 , pp. 6309-6320
    • Lim, S.C.1    Li, M.2    Teo, L.P.3
  • 18
    • 77951086281 scopus 로고    scopus 로고
    • Fractional generalized langevin equation approach to single-file diffusion
    • Eab, CH, Lim, SC: Fractional generalized Langevin equation approach to single-file diffusion. Physica A 389, 2510-2521 (2010)
    • (2010) Physica A , vol.389 , pp. 2510-2521
    • Eab, C.H.1    Lim, S.C.2
  • 20
    • 79961027185 scopus 로고    scopus 로고
    • A jacobi-gauss collocation method for solving nonlinear lane-emden type equations
    • Bhrawy, AH, Alofi, AS: A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations. Commun. Nonlinear Sci. Numer. Simul. 17, 62-70 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 62-70
    • Bhrawy, A.H.1    Alofi, A.S.2
  • 21
    • 62549108678 scopus 로고    scopus 로고
    • Legendre-gauss collocation method for initial value problems of second order ordinary differential equations
    • Guo, B-Y, Yan, J-P: Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations. Appl. Numer. Math. 59, 1386-1408 (2009)
    • (2009) Appl. Numer. Math. , vol.59 , pp. 1386-1408
    • Guo, B.-Y.1    Yan, J.-P.2
  • 22
    • 80052373676 scopus 로고    scopus 로고
    • The use of sinc-collocation method for solving multi-point boundary value problems
    • Saadatmandi, A, Dehghan, M: The use of sinc-collocation method for solving multi-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 17, 593-601 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 593-601
    • Saadatmandi, A.1    Dehghan, M.2
  • 23
    • 84860339097 scopus 로고    scopus 로고
    • On shifted jacobi spectral method for high-order multi-point boundary value problems
    • Doha, EH, Bhrawy, AH, Hafez, RM: On shifted Jacobi spectral method for high-order multi-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 17, 3802-3810 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 3802-3810
    • Doha, E.H.1    Bhrawy, A.H.2    Hafez, R.M.3
  • 24
    • 44149096688 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
    • DOI 10.1016/j.apnum.2007.07.001, PII S0168927407001109
    • Doha, EH, Bhrawy, AH: Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials. Appl. Numer. Math. 58, 1224-1244 (2008) (Pubitemid 351718463)
    • (2008) Applied Numerical Mathematics , vol.58 , Issue.8 , pp. 1224-1244
    • Doha, E.H.1    Bhrawy, A.H.2
  • 25
    • 66049087571 scopus 로고    scopus 로고
    • A jacobi spectral galerkin method for the integrated forms of fourth-order elliptic differential equations
    • Doha, EH, Bhrawy, AH: A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations. Numer. Methods Partial Differ. Equ. 25, 712-739 (2009)
    • (2009) Numer. Methods Partial Differ. Equ. , vol.25 , pp. 712-739
    • Doha, E.H.1    Bhrawy, A.H.2
  • 26
    • 84855235683 scopus 로고    scopus 로고
    • Jacobi discrete approximation for solving optimal control problems
    • El-Kady, M: Jacobi discrete approximation for solving optimal control problems. J. Korean Math. Soc. 49, 99-112 (2012)
    • (2012) J. Korean Math. Soc. , vol.49 , pp. 99-112
    • El-Kady, M.1
  • 27
    • 84858332341 scopus 로고    scopus 로고
    • Efficient spectral-petrov-galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized jacobi polynomials
    • Doha, EH, Abd-Elhameed, WM, Youssri, YH: Efficient spectral-Petrov- Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials. Appl. Math. Comput. 218, 7727-7740 (2012)
    • (2012) Appl. Math. Comput. , vol.218 , pp. 7727-7740
    • Doha, E.H.1    Abd-Elhameed, W.M.2    Youssri, Y.H.3
  • 28
    • 84866665111 scopus 로고    scopus 로고
    • On exponential convergence of gegenbauer interpolation and spectral differentiation
    • in press
    • Xie, Z, Wang, L-L, Zhao, X: On exponential convergence of Gegenbauer interpolation and spectral differentiation. Math. Comput. (2012, in press)
    • (2012) Math. Comput.
    • Xie, Z.1    Wang, L.-L.2    Zhao, X.3
  • 29
    • 80052187663 scopus 로고    scopus 로고
    • Efficient chebyshev spectral method for solving linear elliptic PDEs using quasi-inverse technique
    • Liu, F, Ye, X, Wang, X: Efficient Chebyshev spectral method for solving linear elliptic PDEs using quasi-inverse technique. Numer. Math. Theor. Meth. Appl. 4, 197-215 (2011)
    • (2011) Numer. Math. Theor. Meth. Appl. , vol.4 , pp. 197-215
    • Liu, F.1    Ye, X.2    Wang, X.3
  • 30
    • 84855214521 scopus 로고    scopus 로고
    • Solving fractional nonlinear fredholm integro-differential equations by the second kind chebyshev wavelet
    • Zhu, L, Fan, Q: Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet. Commun. Nonlinear Sci. Numer. Simul. 17, 2333-2341 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 2333-2341
    • Zhu, L.1    Fan, Q.2
  • 31
    • 84864281487 scopus 로고    scopus 로고
    • An efficient direct solver for multidimensional elliptic robin boundary value problems using a legendre spectral-galerkin method
    • doi:10.1016/j.camwa.2011.12.050
    • Doha, EH, Bhrawy, AH: An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method. Comput. Math. Appl. (2012). doi:10.1016/j.camwa.2011.12.050
    • (2012) Comput. Math. Appl.
    • Doha, E.H.1    Bhrawy, A.H.2
  • 34
    • 0037134397 scopus 로고    scopus 로고
    • On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
    • DOI 10.1088/0305-4470/35/15/308, PII S030544700229188X
    • Doha, EH: On the coefficients of differentiated expansions and derivatives of Jacobi polynomials. J. Phys. A, Math. Gen. 35, 3467-3478 (2002) (Pubitemid 37023915)
    • (2002) Journal of Physics A: Mathematical and General , vol.35 , Issue.15 , pp. 3467-3478
    • Doha, E.H.1
  • 35
    • 0742271179 scopus 로고    scopus 로고
    • On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials
    • DOI 10.1088/0305-4470/37/3/010, PII S030544700465565X
    • Doha, EH: On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials. J. Phys. A, Math. Gen. 37, 657-675 (2004) (Pubitemid 38148936)
    • (2004) Journal of Physics A: Mathematical and General , vol.37 , Issue.3 , pp. 657-675
    • Doha, E.H.1
  • 36
    • 84861893481 scopus 로고    scopus 로고
    • A new jacobi operational matrix: An application for solving fractional differential equations
    • doi:10.1016/j.apm.2011.12.031
    • Doha, EH, Bhrawy, AH, Ezz-Eldien, SS: A new Jacobi operational matrix: an application for solving fractional differential equations. Appl. Math. Model. (2012). doi:10.1016/j.apm.2011.12.031
    • (2012) Appl. Math. Model
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.