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Fractional nonlinear Volterra–Fredholm integral equations involving Atangana–Baleanu fractional derivative: framelet applications [PDF]
Advances in Difference Equations, 2020 AbstractIn this work, we propose a framelet method based on B-spline functions for solving nonlinear Volterra–Fredholm integro-differential equations and by involving Atangana–Baleanu fractional derivative, which can provide a reliable numerical approximation. The framelet systems are generated using the set of B-splines with high vanishing moments. We
Mutaz Mohammad, Alexander Trounev
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Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces [PDF]
Arab Journal of Mathematical Sciences, 2021 Purpose – The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces.
Godwin Amechi Okeke, Daniel Francis
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A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations [PDF]
Abstract and Applied Analysis, 2014 A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation ...
Xiaomin Wang
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Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method [PDF]
Tatra Mountains Mathematical Publications, 2021 Abstract In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved ...
Hamani, Fatima, Rahmoune, Azedine
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On the numerical solutions for nonlinear Volterra-Fredholm integral equations
Boletim da Sociedade Paranaense de Matemática, 2022 In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an ...
Darania, Parviz, Pishbin, Saeed
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Fractal and Fractional, 2023 The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim +3 more
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Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra ...
Run Xu, Xiangting Ma
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On some nonlinear retarded Volterra–Fredholm type integral inequalities on time scales and their applications [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we establish some new nonlinear retarded Volterra–Fredholm type integral inequalities on time scales. Our results not only generalize and extend some known integral inequalities, but also provide a handy and effective tool for the study of
Haidong Liu
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Alexandria Engineering Journal, 2013 A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented.
Farshid Mirzaee, Ali Akbar Hoseini
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Fractal and Fractional, 2020 The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM).
Atanaska Georgieva, Snezhana Hristova
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