메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

On a generalized laguerre operational matrix of fractional integration

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY ORDER; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL INTEGRATION; LAGUERRE POLYNOMIAL; MULTI TERMS; OPERATIONAL MATRICES; RIEMANN-LIOUVILLE SENSE; SEMI-INFINITE INTERVALS;

EID: 84876587708     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/569286     Document Type: Article
Times cited : (9)

References (39)
  • 1
    • 36249022993 scopus 로고    scopus 로고
    • San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022 ZBL1056.93542
    • Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering MR1658022 ZBL1056.93542
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 3
    • 77956684069 scopus 로고    scopus 로고
    • Amsterdam, The Netherlands Elsevier Science B.V. North-Holland Mathematics Studies MR2218073 10.1016/S0304-0208(06)80001-0 ZBL1206.26007
    • Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science B.V. xvi+523 North-Holland Mathematics Studies MR2218073 10.1016/S0304-0208(06)80001-0 ZBL1206.26007
    • (2006) Theory and Applications of Fractional Differential Equations , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 4
    • 79953189314 scopus 로고    scopus 로고
    • An approximate analytical solution of time-fractional telegraph equation
    • 10.1016/j.amc.2011.02.030 MR2784584 ZBL1216.65135
    • Das S., Vishal K., Gupta P. K., Yildirim A., An approximate analytical solution of time-fractional telegraph equation. Applied Mathematics and Computation 2011 217 18 7405 7411 10.1016/j.amc.2011.02.030 MR2784584 ZBL1216.65135
    • (2011) Applied Mathematics and Computation , vol.217 , Issue.18 , pp. 7405-7411
    • Das, S.1    Vishal, K.2    Gupta, P.K.3    Yildirim, A.4
  • 6
  • 9
    • 84870945022 scopus 로고    scopus 로고
    • Stability of quadruped robots' trajectories subjected to discrete perturbations
    • 10.1007/s11071-012-0600-2
    • Pinto C. M. A., Stability of quadruped robots' trajectories subjected to discrete perturbations. Nonlinear Dynamics 2012 70 3 2089 2094 10.1007/s11071-012-0600-2
    • (2012) Nonlinear Dynamics , vol.70 , Issue.3 , pp. 2089-2094
    • Pinto, C.M.A.1
  • 10
    • 84871756844 scopus 로고    scopus 로고
    • A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials
    • Jafari H., Tajadodi H., Baleanu D., A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials. Fractional Calculus and Applied Analysis 2013 16 1 109 122
    • (2013) Fractional Calculus and Applied Analysis , vol.16 , Issue.1 , pp. 109-122
    • Jafari, H.1    Tajadodi, H.2    Baleanu, D.3
  • 11
    • 67349108955 scopus 로고    scopus 로고
    • Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease
    • 2-s2.0-67349108955 10.1109/TBME.2008.2004966
    • Ionescu C. M., De Keyser R., Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease. IEEE Transactions on Biomedical Engineering 2009 56 4 978 987 2-s2.0-67349108955 10.1109/TBME.2008.2004966
    • (2009) IEEE Transactions on Biomedical Engineering , vol.56 , Issue.4 , pp. 978-987
    • Ionescu, C.M.1    De Keyser, R.2
  • 12
    • 67149113430 scopus 로고    scopus 로고
    • Mechanical properties of the respiratory system derived from morphologic insight
    • 2-s2.0-67149113430 10.1109/TBME.2008.2007807
    • Ionescu C. M., Segers P., De Keyser R., Mechanical properties of the respiratory system derived from morphologic insight. IEEE Transactions on Biomedical Engineering 2009 56 4 949 959 2-s2.0-67149113430 10.1109/TBME.2008. 2007807
    • (2009) IEEE Transactions on Biomedical Engineering , vol.56 , Issue.4 , pp. 949-959
    • Ionescu, C.M.1    Segers, P.2    De Keyser, R.3
  • 14
    • 79961002199 scopus 로고    scopus 로고
    • Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
    • 10.1016/j.camwa.2011.04.023 MR2824680 ZBL1228.65132
    • Esmaeili S., Shamsi M., Luchko Y., Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials. Computers & Mathematics with Applications 2011 62 3 918 929 10.1016/j.camwa.2011.04.023 MR2824680 ZBL1228.65132
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.3 , pp. 918-929
    • Esmaeili, S.1    Shamsi, M.2    Luchko, Y.3
  • 15
    • 39449122795 scopus 로고    scopus 로고
    • Generalized differential transform method: Application to differential equations of fractional order
    • DOI 10.1016/j.amc.2007.07.068, PII S0096300307007916
    • Odibat Z., Momani S., Erturk V. S., Generalized differential transform method: application to differential equations of fractional order. Applied Mathematics and Computation 2008 197 2 467 477 10.1016/j.amc.2007.07.068 MR2400669 ZBL1221.34022 (Pubitemid 351273764)
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.2 , pp. 467-477
    • Odibat, Z.1    Momani, S.2    Erturk, V.S.3
  • 16
    • 77953683625 scopus 로고    scopus 로고
    • An existence result for a superlinear fractional differential equation
    • 10.1016/j.aml.2010.04.049 MR2659151 ZBL1200.34004
    • Bǎleanu D., Mustafa O. G., Agarwal R. P., An existence result for a superlinear fractional differential equation. Applied Mathematics Letters 2010 23 9 1129 1132 10.1016/j.aml.2010.04.049 MR2659151 ZBL1200.34004
    • (2010) Applied Mathematics Letters , vol.23 , Issue.9 , pp. 1129-1132
    • Bǎleanu, D.1    Mustafa, O.G.2    Agarwal, R.P.3
  • 17
    • 78649549013 scopus 로고    scopus 로고
    • On the solution set for a class of sequential fractional differential equations
    • 10.1088/1751-8113/43/38/385209 MR2718329 ZBL1216.34004 7
    • Bǎleanu D., Mustafa O. G., Agarwal R. P., On the solution set for a class of sequential fractional differential equations. Journal of Physics A 2010 43 38 385209, 7 10.1088/1751-8113/43/38/385209 MR2718329 ZBL1216.34004
    • (2010) Journal of Physics A , vol.43 , Issue.38 , pp. 385209
    • Bǎleanu, D.1    Mustafa, O.G.2    Agarwal, R.P.3
  • 18
    • 84862289566 scopus 로고    scopus 로고
    • Efficient solutions of multidimensional sixth-order boundary value problems using symmetric generalized Jacobi-Galerkin method
    • 10.1155/2012/749370 749370 MR2926876 ZBL1246.65121
    • Doha E. H., Abd-Elhameed W. M., Efficient solutions of multidimensional sixth-order boundary value problems using symmetric generalized Jacobi-Galerkin method. Abstract and Applied Analysis 2012 2012 19 10.1155/2012/749370 749370 MR2926876 ZBL1246.65121
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 19
    • Doha, E.H.1    Abd-Elhameed, W.M.2
  • 19
    • 84866992132 scopus 로고    scopus 로고
    • A Jacobi dual-Petrov Galerkin-Jacobi collocation method for solving Korteweg-de Vries equations
    • 10.1155/2012/418943 418943
    • Bhrawy A. H., Al-Shomrani, A Jacobi dual-Petrov Galerkin-Jacobi collocation method for solving Korteweg-de Vries equations. Abstract and Applied Analysis 2012 2012 16 10.1155/2012/418943 418943
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 16
    • Bhrawy, A.H.1    Al-Shomrani2
  • 20
    • 84867754610 scopus 로고    scopus 로고
    • Numerical solutions of odd order linear and nonlinear initial value problems using shifted Jacobi spectral approximations
    • 10.1155/2012/364360 364360
    • Bhrawy A. H., Alghamdi M. A., Numerical solutions of odd order linear and nonlinear initial value problems using shifted Jacobi spectral approximations. Abstract and Applied Analysis 2012 2012 25 10.1155/2012/364360 364360
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 25
    • Bhrawy, A.H.1    Alghamdi, M.A.2
  • 21
    • 84860339097 scopus 로고    scopus 로고
    • On shifted Jacobi spectral method for high-order multi-point boundary value problems
    • 10.1016/j.cnsns.2012.02.027
    • Doha E. H., Bhrawy A. H., Hafez R. M., On shifted Jacobi spectral method for high-order multi-point boundary value problems. Communications in Nonlinear Science and Numerical Simulation 2012 17 10 3802 3810 10.1016/j.cnsns.2012.02. 027
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.10 , pp. 3802-3810
    • Doha, E.H.1    Bhrawy, A.H.2    Hafez, R.M.3
  • 22
    • 80052684621 scopus 로고    scopus 로고
    • Spectral shifted Jacobi tau and collocation methods for solving fifth-order boundary value problems
    • 823273 10.1155/2011/823273 MR2817267 ZBL1221.65171
    • Bhrawy A. H., Alofi A. S., El-Soubhy S. I., Spectral shifted Jacobi tau and collocation methods for solving fifth-order boundary value problems. Abstract and Applied Analysis 2011 2011 14 823273 10.1155/2011/823273 MR2817267 ZBL1221.65171
    • (2011) Abstract and Applied Analysis , vol.2011 , pp. 14
    • Bhrawy, A.H.1    Alofi, A.S.2    El-Soubhy, S.I.3
  • 23
    • 79959275279 scopus 로고    scopus 로고
    • A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations
    • 947230 10.1155/2011/947230 MR2784393 ZBL1216.65086
    • Doha E. H., Bhrawy A. H., Hafez R. M., A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations. Abstract and Applied Analysis 2011 2011 21 947230 10.1155/2011/947230 MR2784393 ZBL1216.65086
    • (2011) Abstract and Applied Analysis , vol.2011 , pp. 21
    • Doha, E.H.1    Bhrawy, A.H.2    Hafez, R.M.3
  • 24
    • 79959260902 scopus 로고    scopus 로고
    • New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method
    • 837218 10.1155/2011/837218 MR2781569 ZBL1217.65155
    • Bhrawy A. H., Abd-Elhameed W. M., New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method. Mathematical Problems in Engineering 2011 2011 14 837218 10.1155/2011/837218 MR2781569 ZBL1217.65155
    • (2011) Mathematical Problems in Engineering , vol.2011 , pp. 14
    • Bhrawy, A.H.1    Abd-Elhameed, W.M.2
  • 25
    • 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
  • 26
    • 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
  • 27
    • 79961168894 scopus 로고    scopus 로고
    • A quadrature tau method for fractional differential equations with variable coefficients
    • 10.1016/j.aml.2011.06.016 MR2826154
    • 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
    • (2011) Applied Mathematics Letters , vol.24 , Issue.12 , pp. 2146-2152
    • Bhrawy, A.H.1    Alofi, A.S.2    Ezz-Eldien, S.S.3
  • 28
    • 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., Al-Shomrani M. M., A shifted Legendre spectral method for fractional-order multi-point boundary value problems. Advances in Differential Equations 2012 10.1186/1687-1847-2012-8
    • (2012) Advances in Differential Equations
    • Bhrawy, A.H.1    Al-Shomrani, M.M.2
  • 29
    • 31944434650 scopus 로고    scopus 로고
    • Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation
    • DOI 10.1016/j.cam.2004.11.053, PII S0377042705002372, International Conference on Mathematics and its Application
    • Guo B.-Y., Wang L.-L., Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation. Journal of Computational and Applied Mathematics 2006 190 1-2 304 324 10.1016/j.cam.2004.11.053 MR2209510 ZBL1087.65079 (Pubitemid 43189955)
    • (2006) Journal of Computational and Applied Mathematics , vol.190 , Issue.1-2 , pp. 304-324
    • Guo, B.-Y.1    Wang, L.-L.2
  • 30
    • 0002577320 scopus 로고
    • Estimates of Laguerre spectral projectors in Sobolev spaces
    • Basel, Switzerland Baltzer IMACS Ann. Comput. Appl. Math. MR1270241 ZBL0842.46017
    • Funaro D., Brezinski C., Gori L., Ronveaux A., Estimates of Laguerre spectral projectors in Sobolev spaces. Orthogonal Polynomials and Their Applications (Erice, 1990) 1991 9 Basel, Switzerland Baltzer 263 266 IMACS Ann. Comput. Appl. Math. MR1270241 ZBL0842.46017
    • (1991) Orthogonal Polynomials and Their Applications (Erice, 1990) , vol.9 , pp. 263-266
    • Funaro, D.1    Brezinski, C.2    Gori, L.3    Ronveaux, A.4
  • 31
    • 79952361145 scopus 로고    scopus 로고
    • Laguerre polynomial approach for solving linear delay difference equations
    • 10.1016/j.amc.2011.01.112 MR2775723 ZBL1211.65166
    • Gülsu M., Gürbüz B., Öztürk Y., Sezer M., Laguerre polynomial approach for solving linear delay difference equations. Applied Mathematics and Computation 2011 217 15 6765 6776 10.1016/j.amc.2011.01. 112 MR2775723 ZBL1211.65166
    • (2011) Applied Mathematics and Computation , vol.217 , Issue.15 , pp. 6765-6776
    • Gülsu, M.1    Gürbüz, B.2    Öztürk, Y.3    Sezer, M.4
  • 32
    • 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
  • 33
    • 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
  • 34
    • 84866046515 scopus 로고    scopus 로고
    • The operational matrix of fractional integration for shifted Chebyshev polynomials
    • 10.1016/j.aml.2012.01.027
    • 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
    • (2013) Applied Mathematics Letters , vol.26 , Issue.1 , pp. 25-31
    • Bhrawy, A.H.1    Alofi, A.S.2
  • 35
    • 0020802565 scopus 로고
    • Chebyshev series approach to system identification, analysis and optimal control
    • DOI 10.1016/0016-0032(83)90082-0
    • Paraskevopoulos P. N., Chebyshev series approach to system identification, analysis and optimal control. Journal of the Franklin Institute 1983 316 2 135 157 10.1016/0016-0032(83)90082-0 MR717873 ZBL0538.93013 (Pubitemid 13603860)
    • (1983) Journal of the Franklin Institute , vol.316 , Issue.2 , pp. 135-157
    • Paraskevopoulos, P.N.1
  • 36
    • 0022080184 scopus 로고
    • Legendre series approach to identification and analysis of linear systems
    • Paraskevopoulos P. N., Legendre series approach to identification and analysis of linear systems. IEEE Transactions on Automatic Control 1985 30 6 585 589 10.1109/TAC.1985.1103992 MR789333 ZBL0559.93041 (Pubitemid 15597630)
    • (1985) IEEE Transactions on Automatic Control , vol.AC-30 , Issue.6 , pp. 585-589
    • Paraskevopoulos, P.N.1
  • 37
    • 70449394642 scopus 로고    scopus 로고
    • Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals
    • 10.1080/10652460802030672 MR2543760 ZBL1169.42314
    • Doha E. H., Ahmed H. M., El-Soubhy S. I., Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals. Integral Transforms and Special Functions 2009 20 7-8 491 503 10.1080/10652460802030672 MR2543760 ZBL1169.42314
    • (2009) Integral Transforms and Special Functions , vol.20 , Issue.7-8 , pp. 491-503
    • Doha, E.H.1    Ahmed, H.M.2    El-Soubhy, S.I.3
  • 38
    • 77950970934 scopus 로고    scopus 로고
    • The Bernstein operational matrix of integration
    • MR2557992 ZBL1185.41006
    • Singh A. K., Singh V. K., Singh O. P., The Bernstein operational matrix of integration. Applied Mathematical Sciences 2009 3 49-52 2427 2436 MR2557992 ZBL1185.41006
    • (2009) Applied Mathematical Sciences , vol.3 , Issue.49-52 , pp. 2427-2436
    • Singh, A.K.1    Singh, V.K.2    Singh, O.P.3
  • 39
    • 0004073954 scopus 로고
    • Providence, RI, USA American Mathematical Society
    • Szegö G., Orthogonal Polynomials 1959 Providence, RI, USA American Mathematical Society
    • (1959) Orthogonal Polynomials
    • Szegö, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.