scholarly journals Numerical solution of two-dimensional nonlinear Hammerstein fuzzy functional integral equations based on fuzzy Haar wavelets

2017 ◽  
Author(s):  
Svetoslav Enkov ◽  
Atanaska Georgieva
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Functional Integral ◽  
Haar Wavelets ◽  
Two Dimensional ◽  
Functional Integral Equations

scholarly journals Solvability for generalized nonlinear two dimensional functional integral equations via measure of noncompactness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soniya Singh ◽  
Bhupander Singh ◽  
Kottakkaran Sooppy Nisar ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Two Dimensional ◽  
Functional Integral Equations

AbstractIn this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the corresponding results of several authors. We present fascinating examples of equations.

Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amir Ahmad Khajehnasiri ◽  
R. Ezzati ◽  
M. Afshar Kermani
Keyword(s):  
Nonlinear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fractional Integration ◽  
Volterra Integral Equations ◽  
Haar Wavelets ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Numerical Examples

Abstract The main aim of this paper is to use the operational matrices of fractional integration of Haar wavelets to find the numerical solution for a nonlinear system of two-dimensional fractional partial Volterra integral equations. To do this, first we present the operational matrices of fractional integration of Haar wavelets. Then we apply these matrices to solve systems of two-dimensional fractional partial Volterra integral equations (2DFPVIE). Also, we present the error analysis and convergence as well. At the end, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

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