Journal ArticleDOI
Numerical research of nonlinear system of fractional Volterra–Fredholm integral–differential equations via Block-Pulse functions and error analysis
Jiaquan Xie,Mingxu Yi +1 more
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TLDR
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.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2019-01-01. It has received 22 citations till now. The article focuses on the topics: Nonlinear system & Linear system.read more
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An effective scheme for solving system of fractional Volterra–Fredholm integro-differential equations based on the Müntz–Legendre wavelets
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.
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Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind
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.
Journal ArticleDOI
Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations
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.
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Robust H∞ output feedback control for type-2 Takagi-Sugeno fuzzy systems with multiple time-delays and disturbances: A descriptor redundancy approach
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.
Journal ArticleDOI
Correction: Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag
TL;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.
References
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Journal ArticleDOI
Solutions of integral and integro-differential equation systems by using differential transform method
Aytac Arikoglu,Ibrahim Ozkol +1 more
TL;DR: In this study, differential transform method (DTM) is applied to both integro-differential and integral equation systems and further expanded with a formulation to treat Fredholm integrals to show capability and robustness.
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Solving linear integro-differential equations system by using rationalized Haar functions method
TL;DR: Rationalized Haar functions are used to estimate the solution of linear integro-differential equations system to some algebraic equations by using numerical examples to show a good degree of accuracy.
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Numerical solution of the system of Fredholm integro-differential equations by the Tau method
TL;DR: The Tau method for the numerical solution of integro-differential equations systems (IDES) is extended and a brief description of the structure of the Tau program by the Maple software is given.
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Solving linear integro-differential equation system by Galerkin methods with hybrid functions
TL;DR: The hybrid Legendre and Block-Pulse functions on interval [0,1) are used to solve the linear integro-differential equation system, and the quadrature formulae for the calculation of inner products of any functions are constructed.
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Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations
TL;DR: A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations by transforming the IDE system and the given conditions into the matrix equations via Chebyshem collocation points.