This paper proves analytically that synchronization of a class of piecewisecontinuous fractional-order systems can be achieved. Since there are no dedicated numerical methods to integrate differential equations with ...
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This paper proves analytically that synchronization of a class of piecewisecontinuous fractional-order systems can be achieved. Since there are no dedicated numerical methods to integrate differential equations with discontinuous right-hand sides for fractional-order models, Filippov's regularization (Filippov, Differential Equations with Discontinuous Right-Hand Sides, 1988) is applied, and Cellina's Theorem (Aubin and Cellina, Differential Inclusions Set-valued Maps and Viability Theory, 1984;Aubin and Frankowska, Set-valued Analysis, 1990) is used. It is proved that the corresponding initial value problem can be converted to a continuous problem of fractional-order systems, to which numerical methods can be applied. In this way, the synchronization problem is transformed into a standard problem for continuous fractional-order systems. Three examples are presented: the Sprott's system, Chen's system, and Shimizu-Morioka's system.
In this article, we develop an efficient and accurate numerical scheme based on the Crank-Nicolson finite difference method and Haar wavelet analysis to evaluate the numerical solution of the Burgers-Huxley equation. ...
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In this article, we develop an efficient and accurate numerical scheme based on the Crank-Nicolson finite difference method and Haar wavelet analysis to evaluate the numerical solution of the Burgers-Huxley equation. The present method is extended form of Haar wavelet 2D scaling which shows that it is reliable for solving nonlinear partial differential equations. The numerical results are more accurate than other existing methods available in the literature and very close to the exact solution. The Haar basis function is generated from multi-resolution analysis and used to evaluate fast and accurate approximate solutions on the collocation points. The convergence of the proposed method is demonstrated by its error analysis. We compared numerical solutions with the exact solutions and solutions available in the literature. The proposed method is found to be straight forward, accurate with small computational cost and can be easily implemented in mathematical software MATLAB.
In this paper, we prove that a class of piecewisecontinuous autonomous systems of fractional order has well-defined Lyapunov exponents. To do so, based on some known results from differential inclusions of integer or...
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In this paper, we prove that a class of piecewisecontinuous autonomous systems of fractional order has well-defined Lyapunov exponents. To do so, based on some known results from differential inclusions of integer order and fractional order, as well as differential equations with discontinuous right-hand sides, the corresponding discontinuous initial value problem is approximated by a continuous one with fractional order. Then, the Lyapunov exponents are numerically determined using, for example, Wolf's algorithm. Three examples of piecewisecontinuous chaotic systems of fractional order are simulated and analyzed: Sprott's system, Chen's system, and Simizu-Morioka's system.
A universal approximator based on h MOS analog circuits which provides direct analog synthesis of nonlinear functions is described. For this purpose a mathematical approach, founded on rigorous theoretical results and...
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A universal approximator based on h MOS analog circuits which provides direct analog synthesis of nonlinear functions is described. For this purpose a mathematical approach, founded on rigorous theoretical results and able to approximate a continuousfunction with a given small error, is reported. Within the theory it is demonstrated that a piecewise continuous function can be represented with particular sequences of functions, called Dime functions, having certain useful properties. Moreover, it is shown that such functions can be implemented with MOS analog circuits, on the basis of which the architecture of a universal approximator of nonlinear functions is defined.
In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on...
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In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on the corresponding Toeplitz algebra.
Let X be a Hausdorff topological space, and let denote the space of all real Baire-one functions defined on X. Let A be a nonempty subset of X endowed with the topology induced from X, and let be the set of functions ...
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Let X be a Hausdorff topological space, and let denote the space of all real Baire-one functions defined on X. Let A be a nonempty subset of X endowed with the topology induced from X, and let be the set of functions with a property making a linear subspace of . We give a sufficient condition for the existence of a linear extension operator , where means to be piecewisecontinuous on a sequence of closed and subsets of X and is denoted by . We show that restricted to bounded elements of endowed with the supremum norm is an isometry. As a consequence of our main theorem, we formulate the conclusion about existence of a linear extension operator for the classes of Baire-one-star and piecewise continuous functions.
We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results ar...
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We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results are new even in the case of standard Lebesgue spaces and give answers on two questions about algebras of continuous Fourier multipliers on Lebesgue spaces over the real line posed by Mascarenhas, Santos and Seidel.
A mathematical analysis, including existence and uniqueness, is given for some boundary value problems which model the flow of a fluid-solute mixture in a tube which is placed in an interstitium. The model permits an ...
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A mathematical analysis, including existence and uniqueness, is given for some boundary value problems which model the flow of a fluid-solute mixture in a tube which is placed in an interstitium. The model permits an interchange of fluid and solute across the tube walls.
The aim of this paper is to obtain the numerical solution of singular ordinary differential equations using the Haar-wavelet *** proposed method is mathematically simple and provides highly accurate *** this method,we...
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The aim of this paper is to obtain the numerical solution of singular ordinary differential equations using the Haar-wavelet *** proposed method is mathematically simple and provides highly accurate *** this method,we derive the Haar operational matrix using Haar *** operational matrix is a basic tool and applied in system analysis to evaluate the numerical solution of differential *** convergence of the proposed method is discussed through its error *** illustrate the efficiency of this method,solutions of four singular differential equations are obtained.
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