Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
Reads0
Chats0
TLDR
In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.Abstract:
The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s2 + 1), e-s and e-√s etc. are established. Several distributed parameter problems are solved by the new approach.read more
Citations
More filters
Journal ArticleDOI
Haar wavelet method for solving lumped and distributed-parameter systems
C.F. Chen,C.H. Hsiao +1 more
TL;DR: In this article, an operational matrix of integration based on Haar wavelets is established, and a procedure for applying the matrix to analyse lumped and distributed-parameters dynamic systems is formulated.
Journal ArticleDOI
The legendre wavelets operational matrix of integration
TL;DR: In this article, an operational matrix of integration P based on Legendre wavelets is presented, and a general procedure for forming this matrix is given. Illustrative examples are included to demonstrate the validity and applicability of the matrix P.
Journal ArticleDOI
On the role of fractional calculus in electromagnetic theory
TL;DR: In this paper, the concept of fractional derivatives/integrals has been applied in several specific electromagnetic problems, and promising results and ideas that demonstrate that these mathematical operators can be interesting and useful tools in electromagnetic theory.
Journal ArticleDOI
Kronecker operational matrices for fractional calculus and some applications
Adem Kilicman,Zeyad Al Zhour +1 more
TL;DR: The Kronecker convolution product is introduced and expanded to the Riemann-Liouville fractional integral of matrices and several operational matrices for integration and differentiation are studied.
Journal ArticleDOI
Chebyshev series approach to system identification, analysis and optimal control
TL;DR: The Chebyshev series approach appears to have certain advantages over other orthogonal series, and they may therefore be more suitable for the study of the problems of identification, analysis and optimal control.
References
More filters
Journal ArticleDOI
Approximation of Fractional Capacitors (1/s)^(1/n) by a Regular Newton Process
G. Carlson,C. Halijak +1 more
TL;DR: In this article, a third-order Newton process for approximating (l/s) √ 1/n}, the general fractional capacitor, for any integer n > 1 is presented.
Journal ArticleDOI
A state-space approach to Walsh series solution of linear systems
C. F. Chen,C. H. Hsiao +1 more
TL;DR: In this paper, a state-space procedure for solving linear dynamic systems by the Walsh series is developed, where a new operational matrix plays the main role and a new Kronecker product formula is established.
Journal ArticleDOI
Design of piecewise constant gains for optimal control via Walsh functions
Chih-Fan Chen,Chi-Huang Hsiao +1 more
TL;DR: This paper presents a technique for determinating time-varying feedback gains of linear systems with quadratic performance criteria by developing an operational matrix for solving state equations and solving the piecewise constant gains problem.
Journal ArticleDOI
A walsh series direct method for solving variational problems
C.F. Chen,C.H. Hsiao +1 more
TL;DR: In this article, a clear procedure for the variational problem solution via the Walsh functions is established and an operational matrix is derived for integration use, by means of the direct method using the Walsh series.
Journal ArticleDOI
Solution of differential and integral equations with Walsh functions
TL;DR: In this paper, a Walsh series is expressed as a series of Walsh functions, and the coefficients of the input series will change, but there will be no new terms not in the original groups.