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Kronecker operational matrices for fractional calculus and some applications. (English) Zbl 1123.65063

The authors study several operational matrices for integration and differentiation. For some applications, it is often not necessary to compute exact solutions, approximate solutions are sufficient. The given method is extended to find the exact and numerical solutions of the general system matrix convolution differential equations.
Several systems are solved by the new and other approaches, and illustrative examples are considered.

MSC:

65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
26A33 Fractional derivatives and integrals
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[1] Al Zhour Zeyad, Kilicman Adem, Some applications of the convolution and Kronecker products of matrices, in: Proceeding of the International Conference on Math. 2005, UUM, Kedah, Malaysia, 2005, pp. 551-562. · Zbl 1176.15034
[2] Chen, T.; Francis, B.A., Optimal sampled-data control systems, (1995), Springer London · Zbl 0847.93040
[3] Chen, C.F.; Tsay, Y.T.; Wu, T.T., Walsh operational matrices for fractional calculus and their applications to distributed systems, J. frankin inst., 303, 3, 267-284, (1977) · Zbl 0377.42004
[4] A.E. Gilmour, Circulant Matrix Methods for the Numerical solutions of Partial Differential Equations by FFT Convolutions, New Zealand, 1987. · Zbl 0645.65065
[5] Maleknejad, K.; Shaherezaee, M.; Khatami, H., Numerical solution of integral equations systems of second kind by block pulse functions, Appl. math. comput., 166, 15-24, (2005) · Zbl 1073.65149
[6] Mouroutsos, S.G.; Sparis, P.D., Taylor series approach to system identification, analysis and optimal control, J. frankin inst., 319, 3, 359-371, (1985) · Zbl 0561.93018
[7] Nikolaos, L., Dependability analysis of semi-Markov system, Reliab. eng. syst. safety, 55, 203-207, (1997)
[8] Ross, B., Fractional calculus and its applications, (1975), Springer-Verlag Berlin
[9] Sumita, H., The matrix Laguerre transform, Appl. math. comput., 15, 1-28, (1984) · Zbl 0553.44002
[10] Wang, C.-H., On the generalization of block pulse operational matrices for fractional and operational calculus, J. frankin inst., 315, 2, 91-102, (1983) · Zbl 0544.44006
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