Author
Mingxu Yi
Bio: Mingxu Yi is an academic researcher from Beihang University. The author has contributed to research in topics: Orthogonal functions & Nonlinear system. The author has an hindex of 1, co-authored 1 publications receiving 14 citations.
Papers
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TL;DR: A numerical scheme for approximating the solutions of nonlinear system of fractional-order Volterra–Fredholm integral–differential equations (VFIDEs) based on the orthogonal functions defined over 0, 1 combined with their operational matrices of integration and fractional -order differentiation is proposed.
22 citations
Cited by
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TL;DR: Using the Lipschitz’s condition for multivariate functions and the fixed point theorem, the existence and uniqueness of the solution are shown and also convergence, stability and error bound ofThe solution in interval 0, 1 are investigated in this work.
13 citations
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TL;DR: In this paper, the application of polynomial and non-polynomial splines to the solution of nonlinear Volterra integral equations is discussed. And the results of the numerical experiments are presented.
Abstract: The present paper is devoted to the application of local polynomial and non-polynomial
interpolation splines of the third order of approximation for the numerical solution of the Volterra integral
equation of the second kind. Computational schemes based on the use of the splines include the ability to
calculate the integrals over the kernel multiplied by the basis function which are present in the computational
methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra
integral equations is also discussed. The results of the numerical experiments are presented.
11 citations
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TL;DR: In this article, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method.
Abstract: In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in our method. In the established scheme, we approximate the unknown functions by CWs with unknown coefficients and reduce the problem to an algebraic system. In this way, we simplify the computation of nonlinear terms by obtaining some new results for CWs. Finally, we demonstrate the applicability of the presented algorithm by solving a few numerical examples.
10 citations
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TL;DR: The H∞ stability analysis and intervaltype‐2 Takagi‐Sugeno (T‐S) fuzzy control is studied for a class of interval type‐2 T‐S fuzzy systems and two classes of stability conditions in terms of linear matrix inequalities (LMIs) are derived.
9 citations
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01 Jan 2021TL;DR: In this paper, a modified Adomian decomposition method and quadrature rules were used to approximate the solutions of the NV-FIEs of second kind with a phase lag.
Abstract: This study is focused on the numerical solutions of the nonlinear Volterra-Fredholm integral equations (NV-FIEs) of the second kind, which have several applications in physical mathematics and contact problems. Herein, we develop a new technique that combines the modified Adomian decomposition method and the quadrature (trapezoidal and Weddle) rules that used when the definite integral could be extremely difficult, for approximating the solutions of the NV-FIEs of second kind with a phase lag. Foremost, Picard's method and Banach's fixed point theorem are implemented to discuss the existence and uniqueness of the solution. Furthermore, numerical examples are presented to highlight the proposed method's effectiveness, wherein the results are displayed in group of tables and figures to illustrate the applicability of the theoretical results.
9 citations