
doi: 10.3934/mfc.2021013
<p style='text-indent:20px;'>The volterra-fredholm integral equation in all forms are arose from physics, biology and engineering problems which is derived from differential equation modelling. On the other hand, the trained programming algorithm by the fuzzy artificial neural networks has effective solution to find the best answer. In this article we try to estimate the equation and its answer by developed fuzzy artificial neural network to fuzzy volterra-fredholme integral. Our attempts would lead to benchmark other extended forms of this type of equation.</p>
trained algorithm, Volterra integral equations, Fuzzy real analysis, Fredholm integral equations, Numerical methods for integral equations, fuzzy artificial neural network, Artificial neural networks and deep learning, fuzzy Volterra-Fredholm integral equation
trained algorithm, Volterra integral equations, Fuzzy real analysis, Fredholm integral equations, Numerical methods for integral equations, fuzzy artificial neural network, Artificial neural networks and deep learning, fuzzy Volterra-Fredholm integral equation
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