An advanced scheme based on artificial intelligence technique for solving nonlinear riccati systems

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Date

2024

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Springer Heidelberg

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Abstract

Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes effectively with other traditional methods in providing accurate solutions for fractional differential equations (FDEs). This work aims to implement a feedforward ANN with two hidden layers to solve nonlinear systems based on the fractional Riccati differential equation (FRDE). The network parameters are trained using the Adam optimization method with the aid of automatic differentiation. A vectorization algorithm is designated for the selected step to make the computation process more efficient. Two different initial value problems in integer-order derivatives and fractional-order derivatives are discussed. Numerical results demonstrate that the proposed method not only closely matches the exact solutions and reference solutions but also is more accurate than other existing methods.

Description

Ahmadian, Ali/0000-0002-0106-7050

Keywords

Artificial neural network, Fractional riccati differential equation, Adam optimization method, Vectorization algorithm

Turkish CoHE Thesis Center URL

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0

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Q1

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Q1

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Volume

43

Issue

6

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