Fractional Differential Equations

In this paper, an improved ant colony optimization (ICMPACO) algorithm based on the multi-population strategy, co-evolution mechanism, pheromone updating strategy, and pheromone diffusion mechanism is proposed to balance the convergence speed and solution diversity, and improve the optimization performance in solving the large-scale optimization problem. In the proposed ICMPACO algorithm, the optimization problem is divided into several sub-problems and the ants in the population are divided into elite ants and common ants in order to improve the convergence rate, and avoid to fall into the local optimum value. The pheromone updating strategy is used to improve optimization ability. The pheromone diffusion mechanism is used to make the pheromone released by ants at a certain point, which gradually affects a certain range of adjacent regions. The co-evolution mechanism is used to interchange information among different sub-populations in order to implement information sharing. In order to verify the optimization performance of the ICMPACO algorithm, the traveling salesmen problem (TSP) and the actual gate assignment problem are selected here. The experiment results show that the proposed ICMPACO algorithm can effectively obtain the best optimization value in solving TSP and effectively solve the gate assignment problem, obtain better assignment result, and it takes on better optimization ability and stability.

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An Improved Ant Colony Optimization Algorithm Based on Hybrid Strategies for Scheduling Problem

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontin- uous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational itera- tion method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effec- tive analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional com- plex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

A fractional epidemiological model for computer viruses pertaining to a new fractional derivative

A new computational approach for solving nonlinear local fractional PDEs

We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

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Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

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Local fractional series expansion method for solving wave and diffusion equations on Cantor sets

Synthesis and comparison of photocatalytic properties for Bi2WO6 nanofibers and hierarchical microspheres

Medical images play a very important role in making the right diagnosis for the doctor and in the patient’s treatment process. Using intelligent algorithms makes it possible to quickly distinguish the lesions of medical images, and it is especially important to extract features from images. Many studies have integrated various algorithms into medical images. For medical image feature extraction, a large amount of data is analyzed to obtain processing results, helping doctors to make more accurate case diagnosis. In view of this, this paper takes tumor images as the research object, and first performs local binary pattern feature extraction of the tumor image by rotation invariance. As the image shifts and the rotation changes, the image is stationary relative to the coordinate system. The method can accurately describe the texture features of the shallow layer of the tumor image, thereby enhancing the robustness of the image region description. Focusing on image feature extraction based on convolutional neural network (CNN), the basic framework of CNN is built. In order to break the limitations of machine vision and human vision, the research is extended to multi-channel input CNN for image feature extraction. Two convolution models of Xception and Dense Net are built to improve the accuracy of the CNN algorithm. It can be seen from the experimental results that the CNN algorithm shows high accuracy in tumor image feature extraction. In this paper, the CNN algorithm is compared with several classical algorithms in the local binary mode. The CNN algorithm has more accurate feature extraction ability for tumor CT images on a larger data basis. Furthermore, the advantages of CNN algorithms in this field are demonstrated.

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Research on Feature Extraction of Tumor Image Based on Convolutional Neural Network

Titanium alloy has been widely applied in industrial engineering products due to its advantages of great corrosion resistance and high specific strength. This paper investigated the processing parameters for finish turning of titanium alloy TC11. Firstly, a three-factor central composite design of experiment, considering the cutting speed, feed rate and depth of cut, are conducted in titanium alloy TC11 and the corresponding surface roughness are obtained. Then a mathematic model is constructed by the response surface methodology to fit the relationship between the process parameters and the surface roughness. The prediction accuracy was verified by the one-way ANOVA. Finally, the contour line of the surface roughness under different combination of process parameters are obtained and used for the optimum surface roughness prediction. Verification experimental results demonstrated that material removal rate (MRR) at the obtained optimum can be significantly improved without sacrificing the surface roughness.

Ai-Min Yang

Papers

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

Local fractional series expansion method for solving wave and diffusion equations on Cantor sets

Synthesis and comparison of photocatalytic properties for Bi2WO6 nanofibers and hierarchical microspheres

Research on Feature Extraction of Tumor Image Based on Convolutional Neural Network

Optimum surface roughness prediction for titanium alloy by adopting response surface methodology