A new fractional Abel polynomials neural network method for nonlinear models of heat transfer

Abstract

Nowadays, the study and advancements in neural networks and optimization techniques are the most interesting research topics. This progress has empowered researchers to address more intricate and realistic challenges associated with nonlinear models. This research presents a new approach called the fractional Abel polynomials neural network (FAPNN) for solving nonlinear heat transfer models. The mentioned NN consists of three layers (input layer, hidden layer, output layer). Fractional Abel and arcsinh(t) functions have been used as activation functions in the hidden and output layers, respectively, to construct the FAPNN. To mitigate storage and computational costs, new operational matrices (OMs) are devised. Based on FAPNN and OMs for fractional Abel polynomials, a series solution is achieved for the nonlinear heat transfer models. The Lagrange multipliers method is adopted so that the nonlinear heat transfer models can be transformed into a class of nonlinear algebraic system of equations and we solve these equations using Matlab and Maple software. Ultimately, four sets of numerical examples are provided along with comparisons from the literature such as the variational iteration, homotopy perturbation, differential transformation, and Chebyshev wavelets methods, to confirm the effectiveness of the suggested FAPNN approach. Experimental results demonstrate the effectiveness of our proposed method.