Design an intelligent system for solving two-dimensional fuzzy singular perturbed mixed Volterra - Fredholm integro-Partial differential equations

Recently, the study of fuzzy singular perturbed Mixed Volterra - Fredholm integro-Partial differential equations (FSPMV-FIPDE) has been of increasing interest for a long time. Our paper has a design for a fast feed - forward neural network to adduce a new method for solving two-dimensions (FSPMV-FIPDE). Employing a multi-layer that has one hidden layer with five units and one linear output unit. And the sigmoid activation for every unit is the hyperbolic tangent function and the Levenberg – Marquardt training algorithm. We compared our exact solution in illustrative examples with the results of numerical experiments, confirming the efficiency and accuracy of our presented scheme.