In this paper, we use hybrid parabolic and block-pulse functions (2D-PBPFs) to provide an approximate solution of nonlinear partial mixed Volterra-Fredholm integro-differential equations of fractional order. To reach ...
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In this paper, we use hybrid parabolic and block-pulse functions (2D-PBPFs) to provide an approximate solution of nonlinear partial mixed Volterra-Fredholm integro-differential equations of fractional order. To reach this goal, we present the Volterra integral operational matrix, operational matrix of fractional integral and operational matrix of mixed VolterraFredholm integral by 2D-PBPFs. Using the proposed method, nonlinear partial mixed Volterra-Fredholm integro-differential equations of fractional order become into a nonlinear system of algebraic equations. Moreover, we provide some theorems for convergence analysis and we demonstrate that the convergence order of the suggested approximate approach is Ooh3THORN. Finally, we solve two numerical examples to prove the accuracy of the proposed method.
Direct methods are applied to solve linear time-varying delay systems based on vector forms of block-pulse functions (BPFs) and triangular functions (TFs). Operational matrices of integration of BPFs and TFs are appli...
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Direct methods are applied to solve linear time-varying delay systems based on vector forms of block-pulse functions (BPFs) and triangular functions (TFs). Operational matrices of integration of BPFs and TFs are applied to transform linear time-varying delay systems to a linear set of algebraic equations. Further, some numerical examples are provided to indicate reliability and the accuracy of these methods. Convergence analysis of the proposed method has been discussed.
In this work, based on the operational matrix of fractional order integration, we present an approach for the numerical solution of strongly nonlinear full fractional Duffing equation. For this goal, with respect to t...
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In this work, based on the operational matrix of fractional order integration, we present an approach for the numerical solution of strongly nonlinear full fractional Duffing equation. For this goal, with respect to the Caputo derivative, we use the block-pulse wavelets matrix of fractional order integration. To obtain this purpose, the errors are analyzed. The method has been considered by some numerical examples and variations in coefficients as well as in the derivative of the equation too. We examine the exact solutions for the equation under study in three different categories including, polynomials, exponential and sinusoidal solutions. It is shown that the suggested method works well.
This work, we studied the Bratu differential equation of the fractional-order, numerically via introducing a hybrid method. This method is a combination of the Chebyshev polynomials and the block-pulse wavelets matrix...
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This is a review on certain major scientific errors in the paper (Mirzaee, 2014). Beginning with a review of these errors, attempts are made to correct them by presenting an accurate approach and proposing relevant fo...
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This is a review on certain major scientific errors in the paper (Mirzaee, 2014). Beginning with a review of these errors, attempts are made to correct them by presenting an accurate approach and proposing relevant formulas for replacement. Moreover, the method after these corrections is illustrated through some numerical examples and the results are presented.
This is a review on the published paper (Mirzaee and Hoseini, 2013), where there are some major scientific errors. After considering these errors, we attempt to correct them by presenting an accurate formula. In addit...
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This is a review on the published paper (Mirzaee and Hoseini, 2013), where there are some major scientific errors. After considering these errors, we attempt to correct them by presenting an accurate formula. In addition, to illustrate how the method works in practice after our correction, we introduce some numerical examples and present the corresponding results. Finally, we have a short review on the paper (Mirzaee and Hoseini, 2014) by the same authors. The same scientific errors are occurred in this paper, motivating us to correct them, as well. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
In this paper, we present and investigate the analytical properties of a new set of orthogonal basis functions derived from the block-pulse functions. Also, we present a numerical method based on this new class of fun...
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In this paper, we present and investigate the analytical properties of a new set of orthogonal basis functions derived from the block-pulse functions. Also, we present a numerical method based on this new class of functions to solve nonlinear Volterra-Fredholm integral equations. In particular, an alternative and efficient method based on the formalism of artificial neural networks is discussed. The efficiency of the mentioned approach is theoretically justified and illustrated through several qualitative and quantitative examples.
In this paper,we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of *** this,we use the block-puls...
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In this article a robust approach for solving mixed nonlinear Volterra-Fredholm type integral equations of the first kind is investigated. By using the modified two-dimensional block-pulse functions (M2D-BFs) and thei...
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This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero refe...
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ISBN:
(纸本)9781728105215
This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over blockpulsefunctions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.
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