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Original Articles

Laguerre operational matrices for fractional calculus and applications

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Pages 577-584 | Received 04 Mar 1981, Published online: 12 Mar 2007

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Xinxiu Li. (2014) Operational method for solving fractional differential equations using cubic B-spline approximation. International Journal of Computer Mathematics 91:12, pages 2584-2602.
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S.-L. Chen, H.-C. Lai & K.-C. Ho. (2006) Identification of linear time varying systems by Haar wavelet. International Journal of Systems Science 37:9, pages 619-628.
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H. R. Karimi. (2006) A computational method for optimal control problem of time-varying state-delayed systems by Haar wavelets. International Journal of Computer Mathematics 83:2, pages 235-246.
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H. R. Karimi, P. Jabedar Maralani, B. Moshiri & B. Lohmann. (2005) Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets. International Journal of Computer Mathematics 82:4, pages 495-507.
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H. R. Karimi, B. Lohmann, P. Jabedar Maralani & B. Moshiri. (2004) A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets. International Journal of Computer Mathematics 81:9, pages 1121-1132.
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CHING-TIEN LIOU & CHENG-HSIN LIN. (1991) Applications of the methods of weighted residuals in system science. International Journal of Systems Science 22:9, pages 1509-1525.
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V Ranganathan, A N Jha & V S Rajamani. (1991) On-Line Least-Squares Method of Estimating the Coefficients of the Orthogonal-Polynomial Expansion of a Function. IETE Journal of Research 37:3, pages 280-284.
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SHUH-CHUAN TSAY & I-CHANG JOU. (1989) VLSI implementation of state-space equation solver. International Journal of Systems Science 20:8, pages 1441-1450.
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MOHSEN RAZZAGHI & MEHDI RAZZAGHI. (1989) Functional approximation for inversion of Laplace transforms via polynomial series. International Journal of Systems Science 20:7, pages 1131-1139.
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MEHDI RAZZAGHI & MOHSEN RAZZAGHI. (1989) Shifted-Jacobi series direct method for variational problems. International Journal of Systems Science 20:7, pages 1119-1129.
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P. N. PARASKEVOPOULOS. (1989) A new orthogonal series approach to state-space analysis and identification. International Journal of Systems Science 20:6, pages 957-970.
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M. RAZZAGHI & M. RAZZAGHI. (1988) Fourier series direct method for variational problems. International Journal of Control 48:3, pages 887-895.
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Z. H. JIANG. (1987) New approximation method for inverse Laplace transforms using block-pulse functions. International Journal of Systems Science 18:10, pages 1873-1888.
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CHYI HWANG & KUO-KAI SHYU. (1987) Analysis and identification of discrete-time systems via discrete Legendre orthogonal polynomials. International Journal of Systems Science 18:8, pages 1411-1423.
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MAW-LING WANG, RONG-YEU CHANG & SHWU-YIEN YANG. (1987) Generalization of generalized orthogonal polynomial operational matrices for fractional and operational calculus. International Journal of Systems Science 18:5, pages 931-943.
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V. RANGANATHAN, A. N. JHA & V. S. RAJAMANI. (1987) Identification of distributed linear time-varying systems via Laguerre polynomials. International Journal of Systems Science 18:4, pages 681-685.
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HUNG-YUAN CHUNG. (1987) Solution of state-space equations via Fourier series. International Journal of Systems Science 18:2, pages 221-228.
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TSU-TIAN LEE & SHUH-CHUAN TSAY. (1986) Analysis of linear time-varying systems and bilinear systems via shifted Chebyshev polynomials of the second kind. International Journal of Systems Science 17:12, pages 1757-1766.
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YIH-FONG CHANG & TSU-TIAN LEE. (1986) General orthogonal polynomials analysis of linear optimal control systems incorporating observers. International Journal of Systems Science 17:11, pages 1521-1535.
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PANAGIOTISD. SPARIS & SPYRIDONG. MOUROUTSOS. (1986) The operational matrix of differentiation for orthogonal polynomial series. International Journal of Control 44:1, pages 1-15.
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DONG-HER SHIH, FAN-CHU KUNG & CHIEN-MING CHAO. (1986) Laguerre series approach to the analysis of a linear control system incorporating observers. International Journal of Control 43:1, pages 123-128.
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RONG-YEU CHANG, KUN-CHOU CHEN & MAW-LING WANG. (1985) A new approach to the parameter estimation of linear time-invariant delayed systems via modified Laguerre polynomials. International Journal of Systems Science 16:12, pages 1505-1515.
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CHENG-CHIIAN LIU & YEN-PING SHIH. (1985) System analysis, parameter estimation and optimal regulator design of linear systems via Jacobi series. International Journal of Control 42:1, pages 211-224.
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A. N. JHA & S. ZAMAN. (1985) Identification of linear distributed systems using Laguerre operational matrices. International Journal of Systems Science 16:6, pages 761-767.
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CHENG-CHIIAN LIU & YEN-PING SHIH. (1985) Analysis and parameter identification of linear systems via Chebyshev polynomials of the second kind. International Journal of Systems Science 16:6, pages 753-759.
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S. ZAMAN & A. N. JHA. (1985) Parameter identification of non-linear systems using Laguerre operational matrices. International Journal of Systems Science 16:5, pages 625-631.
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RONG-YEU CHANG & MAW-LING WANG. (1985) Solutions of integral equations via shifted Legendre polynomials. International Journal of Systems Science 16:2, pages 197-208.
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JYH-HORNG CHOU & ING-RONG HORNG. (1985) Application of Chebyshev polynomials to the optimal control of time-varying linear systems. International Journal of Control 41:1, pages 135-144.
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MAW-LING WANG, KEWI-SHANG CHEN & CHIH-KAO CHOU. (1984) Solutions of integral equations via modified Laguerre polynomials. International Journal of Systems Science 15:6, pages 661-672.
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CHENG-CHIIAN LIU & YEN-PING SHIH. (1983) Analysis and optimal control of time-varying systems via Chebyshev polynomials. International Journal of Control 38:5, pages 1003-1012.
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Yen‐Min Shih. (1983) Application of chebyshev polynomials in analysis and identification of linear systems. Journal of the Chinese Institute of Engineers 6:2, pages 135-140.
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Yuanlu Li & Ning Sun. (2011) Numerical solution of fractional differential equations using the generalized block pulse operational matrix. Computers & Mathematics with Applications 62:3, pages 1046-1054.
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M.R. Eslahchi & Mehdi Dehghan. (2011) Application of Taylor series in obtaining the orthogonal operational matrix. Computers & Mathematics with Applications 61:9, pages 2596-2604.
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R. Kalpana & S. Raja Balachandar. (2007) Haar wavelet method for the analysis of transistor circuits. AEU - International Journal of Electronics and Communications 61:9, pages 589-594.
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H. R. Karimi, P. J. Maralani, B. Lohmann & B. Moshiri. (2006) Haar wavelet-based optimal control of time-varying state-delayed systems: A computational method. Haar wavelet-based optimal control of time-varying state-delayed systems: A computational method.
H. R. Karimi & B. Lohmann. (2006) A computational method to robust vibration control of vehicle engine-body system using Haar wavelets. A computational method to robust vibration control of vehicle engine-body system using Haar wavelets.
Y.-C. Cheng & C. Hwang. (2006) Use of the Lambert W function for time-domain analysis of feedback fractional delay systems. IEE Proceedings - Control Theory and Applications 153:2, pages 167-174.
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H.R. Karimi, P. Jabedar Maralani, B Moshiri & B Lohmann. (2005) APPROXIMATED OPTIMAL CONTROL OF SINGULARLY PERTURBED SYSTEMS VIA HAAR WAVELETS. IFAC Proceedings Volumes 38:1, pages 353-358.
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H.R. Karimi, P.J. Maralani, B. Moshiri & B. Lohmann. (2005) Haar Wavelet-Based Optimal Control of Time-Varying State-Delayed Systems: A Computational Method. Haar Wavelet-Based Optimal Control of Time-Varying State-Delayed Systems: A Computational Method.
P.N. Paraskevopoulos, P.G. Sklavounos & D.A. Karkas. (1990) A new orthogonal series approach to sensitivity analysis. Journal of the Franklin Institute 327:3, pages 419-433.
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Y. Endow. (1989) Optimal control via Fourier series of operational matrix of integration. IEEE Transactions on Automatic Control 34:7, pages 770-773.
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P. Paraskevopoulos. (1987) The operational matrices of integration and differentiation for the Fourier sine-cosine and exponential series. IEEE Transactions on Automatic Control 32:7, pages 648-651.
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Panagiotis D. Sparis & Spyridon G. Mouroutsos. (1987) Output sensitivity analysis of time-varying linear systems using polynomial series. Journal of the Franklin Institute 324:1, pages 173-185.
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Chyi Hwang & Kuo-Kai Shyu. (1987) Analysis of time-varying discrete systems using discrete legendre orthogonal polynomials. Journal of the Franklin Institute 324:1, pages 149-164.
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Tsu-Tian Lee, Shuh-Chuan Tsay & Ing-Rong Horng. (1986) Shifted-Jacobi Series Analysis of Linear Optimal Control Systems Incorporating Observers. Journal of the Franklin Institute 321:5, pages 289-298.
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P.N. Paraskevopoulos. (1985) System analysis and synthesis via orthogonal polynomial series and fourier series. Mathematics and Computers in Simulation 27:5-6, pages 453-469.
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Ming-Jong Tsai, Cha'o-Kuang Chen & Fan-Chu Kung. (1984) Analysis of linear time-varying systems by shifted legendre polynomials. Journal of the Franklin Institute 318:4, pages 275-282.
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P.N. Paraskevopoulos. (1983) Chebyshev series approach to system identification, analysis and optimal control. Journal of the Franklin Institute 316:2, pages 135-157.
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Fan-Chu Kung & Hua Lee. (1982) Solution of linear state-space equations and parameter estimation in feedback systems using laguerre polynomial expansion. Journal of the Franklin Institute 314:6, pages 393-403.
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