Artificial intelligence algorithms accumulate a large amount of user data through such network platforms, the values of AI algorithm controllers (and in many cases developers) are thus deeply embedded in the supposedly neutral technology, and quietly affect the audience's ideas, decisions and behavior patterns. Through continuous machine learning, algorithms have achieved huge advantages over humans in data capture, learning, and push, and thus strengthen the impact on the audience. Including platform media such as Toutiao and social platforms such as WeChat, are actively using artificial intelligence algorithms to increase user stickiness, and increase market penetration. It is different from the news manual filtering and pushing mechanism in the traditional media era, and it is also different from the news social filtering mechanism in the social network era, AI algorithm recommendation mechanism in the era of big data, with stronger data capture ability and learning ability, the scale and efficiency of information push increase exponentially.
The advent of artificial intelligence algorithms has revolutionized this. Relying on the application of big data technology, the artificial intelligence algorithm is based on the user's behavior data  such as browsing content, forwarding, comments, etc., and deep machine learning and algorithm analysis of identity data, accurately identify and push information about value needs and related preferences for each user, that is, “Only what you pay attention to is the headline.” On this basis, artificial intelligence algorithm recommendations are based on different value preferences and information needs, divide users into multiple overlapping groups, and push the required information for them respectively, realize big data filtering which is different from Moments filtering, so that users can control the capture and reception of information more freely [1]. Fractional calculus is used to describe the memory and genetic properties of various materials and processes, provides a powerful tool, it has been used in many scientific and engineering fields, such as viscoelasticity, anomalous diffusion, fluid mechanics, biology, chemistry, acoustics, control theory, etc. In this way, fractional differential equations, which are class of integraldifferential equations with singularity, naturally appear in applied research. The existence and uniqueness theorem for solutions of fractional ordinary differential equations has been proposed. For linear fractional differential equations, the commonly used integral transformation method, including Laplace transform, Fourier transform and Mellin transform, the analytical solution of the problem is obtained.
There are two commonly used numerical algorithms for nonlinear fractional differential equations, they are the predictioncorrection solution and the timefrequency domain conversion algorithm, respectively. The former method is a classical calculation method, which is a generalization of the AdamaBashforthMoulton method for solving firstorder differential equations, it is widely used in practical fractional order calculations. The latter method includes approximation methods implemented by continuous fractionation, expansion and interpolation, and approximation methods implemented by curve fitting stage identification techniques.
Decomposition methods have been effectively used to solve linear or nonlinear fractional differential equations. The numerical format of the decompositionbased fractional differential equation is given in [1], the ADMPade approximation technique is also used in fractional differential equations, the RachAdomianMeyers modified decomposition method is extended to solve nonlinear fractional differential equations. Other analytical and numerical methods for nonlinear fractional differential equations can be found in [2].
We consider the initial value problem of nonlinear fractional ordinary differential equations Table 1 Properties of independent variables:
Iterative Shanks transform






















We decompose the solution into
Substituting the solution and the decomposition of the nonlinear term into equation (3), we get:
From this we obtain the recursive form of the solution components:
Or apply the recursive format modified by Wazwaz:
Here we decompose the system input as:
The approximate solution for term
Next we consider the RachAdomian Meyers modified decomposition method. For initial value problems (1) and (2), if
We note that every function
Pick:
In this way (13) satisfies the initial value condition (2), then, the nonlinear term is written as:
Calculating the fractional derivatives item by item, we have:
Substituting Equations (12), (15) and (16) into Equation (1), and comparing the coefficients of the same power, we obtain the recurrence format of the coefficient
The approximate solution for term
Accelerated Convergence Techniques are used to accelerate the convergence of sequences or series, and even extend the domain of convergence. In this article, we use iterative Shanks, for example, we obtain the approximate sequence Φ_{1}(
Table 1 shows the transformation process, and
Artificial intelligence neural network includes input layer, hidden layer and output layer, each layer is composed of multiple neuron nodes. The hidden layer can be one layer or multiple layers. Although the hidden layer is not connected to the outside world, its state is crucial, to a considerable extent, it directly affects the mapping relationship between input and output. Many scholars have proved that the threelayer neural network that only contains the input layer, the hidden layer and the output layer already has a strong approximation ability [3].
The learning of artificial intelligence neural network belongs to supervised learning, the learning process consists of two parts: signal forward propagation and error back propagation. The basic training process is to input sample data from the input layer, and then input it to the output layer after implicit, and finally output by the output layer. Both the hidden layer and the output layer have differentiable excitation functions, and the output of each layer of neurons will only affect the output of the next layer of neurons. In the process of data forward propagation, the weights and thresholds of the network will not change. If the output is different from the expected value, the error is backpropagated. The neural network adjusts the connection weights of each layer through the error, and so on, until the error meets the requirements.
The sample data is input from the input layer to the hidden layer, and the input of a single node t of the hidden layer is:
The output of the hidden layer node t is:
The data is then input from the hidden layer to the output layer, and the input of a single node k of the output layer is:
The output of the output layer node k is:
Where
In the initial stage, there is an error between the actual output value of the network and the expected value. In actual data training, the calculation formula of error usually adopts the square error formula, namely formula (25).
The final stable state of the artificial intelligence neural network is that the actual output value is the same or infinitely close to the expected value. Therefore, in the training of the data, it is necessary to constantly modify the connection weights and thresholds of the neural network. The weight correction formula of the neural network adopts the gradient descent method, and its essence is a simple static optimization algorithm of steepest descent [4].
Where u is the weight correction coefficient, that is, the learning rate. The size of the learning rate affects the convergence speed of the algorithm. If the learning rate is too small, the network will converge very slowly. If the learning rate is too large, the network will oscillate and fail to converge. In the classical network algorithm, in each iteration, an accurate onedimensional search is required to obtain the optimal iterative step size. However, onedimensional search requires multiple calculations, which consumes a lot of computing time and is difficult to program and apply. Therefore, onedimensional search is generally not used to optimize the learning rate, but a certain value of 01 is used.
The size of the initial weights also affects the learning rate. Usually the initial weights will choose positive and negative decimals near 0, preferably random and uniform distribution, which can expand the search range of the optimal weights.
The partial derivative of the error E to the weight W in equations (26–27) is also called the weight correction of one iteration. The weight correction amount can be decomposed into a relationship with the input of the hidden layer or the input of the output layer, and easy to calculate fractions. Substitute equations (21) and (22) into the weight corrections of the input layer and hidden layer weights
In MATLAB, run the integer order artificial intelligence neural network program, the number of samples is 30, and get Figure 1 and Figure 2, the abscissa is the number of iteration steps, the ordinate is the training error, P is the number of neurons in the hidden layer, u is the learning rate. Figure 1 shows that the artificial intelligence neural network has the same number of neurons in the hidden layer, under the conditions of different learning rates, training on the same set of data. Figure 2 shows that the artificial intelligence neural network has the same learning rate, under the condition that the number of neurons in the hidden layer is different, training on the same set of data [5]. It can be seen from Figure 1 that the smaller the learning rate, the slower the network convergence speed. Figure 2 shows that there are too many neurons in the hidden layer, which makes the convergence rate very slow, the convergence is very poor, but it is not that the fewer the number of neurons, the smaller the convergence error of the network. Only with the appropriate number of neurons, will get better convergence and less convergence error.
In this section, the node function of the neural network selects the Sigmoid function, because the output of this function is close to the signal output form of biological neurons, it can simulate the nonlinear characteristics of biological neurons. Moreover, the nonlinear characteristics of the sigmoid function, it can also enhance the nonlinear mapping ability of neural network [8].
The mathematical expression of the sigmoid function is:
The first derivative expression of the sigmoid function is:
Considering the hope that the artificial intelligence neural network itself, it can transform the derivative order according to the change of the convergence error, and realize the global selfadaptation, that is, construct the selfadaptive artificial intelligence neural network. When the error between the previous iteration and the next iteration is quite different, the fractional order takes the smaller value, in order to ensure that the network can learn at a relatively fast speed, and in order to prevent network training saturation, that is, the error does not drop but rises, and the magnitude of the adjustment of the fractional order before and after is slightly larger [9, but considering the training process of artificial intelligence neural network, by adjusting the two parameters
When
When
Taking equation (26) as the node function of the fractional artificial neural network, by changing the parameters
When
Through the training of fractionalorder artificial intelligence neural network based on sigmoid function, the effects of fractional order, learning rate and the number of neurons in the hidden layer on its training are summarized. Comparing the training results of the fractionalorder artificial intelligence neural network with the integerorder artificial intelligence network, summarize the advantages and disadvantages of each. On this basis, a variableorder iterative algorithm is proposed, that is, the switching between integer order and fractional order, and the fractional order adaptively adjusts the two algorithms according to the error before and after. Through the actual network training results, the advantages of the algorithm are obtained, and a fractionalorder artificial intelligence network based on this function is constructed for training, summarize the effect of two parameters in the function on network training, and make a simple comparison with the network based on the sigmoid function.
The author mainly studies the algorithm and application of computer artificial intelligence neural network based on fractional calculus theory. The author introduced fractional order theory into the algorithm of computer artificial intelligence neural network, the fractionalorder artificial network algorithm is derived from the two fractionalorder definitions, and the neural network is trained by using a specific data sample set, and compared with the training results of the integer order neural network, the simulation results show that, the fractionalorder computer artificial intelligence neural network has a faster training speed, but it is slightly insufficient in the convergence accuracy. Therefore, a variableorder iterative learning algorithm is proposed and applied to the training of neural networks, the results show that, the feasibility of this algorithm and its advantages in convergence speed and convergence accuracy.
However, the latter variableorder iterative algorithm proposed by the author, it is to adjust the fractional order adaptively according to the ratio of the error before and after. Although the training effect of artificial intelligence network is good, it is too simple, and for different sample sets, some data in the algorithm may need to be modified. Therefore, it is necessary to find a better and more widely used order adjustment algorithm.
Iterative Shanks transform






















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