The authors have developed an efficient method with the Fibonacci neural network’s help to solve the fractional-order reaction-diffusion equation in the present article. The Fibonacci neural network consists of an input layer with one perceptron, a hidden layer with \(n\times m\) perceptions, and an output layer with one perceptron. The authors have used various degrees of the Fibonacci polynomial as an activation function to the input in the hidden layer. The authors then convert the fractional order diffusion equation with initial and boundary conditions into a non-constrained optimization problem, which is then called the cost function. Marquardt’s method is used to update the values of weights to minimize the cost function. After that, the authors used the discussed method on four examples with an exact solution and showed that our method works more accurately than previously existing methods through comparison. In the last, authors have used the discussed method to solve the unsolved diffusion equation and observe the change in solute concentration for different fractional-order at different times.

作者开发了一种利用斐波那契神经网络的有效方法来解决本文中的分数阶反应扩散方程。Fibonacci神经网络由一个带有一个感知器的输入层，一个带有\（n \ times m \）的隐藏层组成感知，以及带有一个感知器的输出层。作者已将斐波那契多项式的不同程度用作隐藏层中输入的激活函数。然后，作者将具有初始和边界条件的分数阶扩散方程式转换为非约束优化问题，然后将其称为成本函数。Marquardt的方法用于更新权重值以最小化成本函数。之后，作者在四个示例上使用了讨论的方法并给出了精确的解决方案，并通过比较表明我们的方法比以前的现有方法更准确地工作。最后，作者使用所讨论的方法求解未解决的扩散方程，并观察了在不同时间不同分数阶的溶质浓度变化。