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Fractional order partial differential equations have a wide range of applications in image processing. The solution of partial differential equations is generally obtained using the finite difference method, which still requires improvement in terms of efficiency and effectiveness. In this work, a multi‐scale interpolative wavelet operator is constructed by means of Shannon‐Cosine wavelets with interpolation, smoothness, compact support and other excellent properties. We use the wavelet operator instead of the finite difference operator to solve fractional‐order partial differential equations. The proposed method can limit the artefacts and remove the noises appeared in the processed images effectively. In addition, for the loss of texture in the denoised image, we enhance the image by employing fractional order differential equations to improve the quality of the image. Finally, the biological sections images are taken as the examples to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Medium frequency transformer (MFT) plays a key role in future power systems and new energy systems. It is very important for the safe operation of MFT to correctly calculate the temperature rise and hot spot position. According to the heat dissipation of transformer, the equivalent thermal network model of the core-type transformer is established in this paper. The traditional thermal network model ignores the heat dissipation of the magnetic core column and the inner surface of the yoke to the air. In this paper, the magnetic core column is divided into the air surrounding part and winding surrounding part. The heat dissipation on the inner surface of the yoke is further considered. The improved thermal network model is verified by finite element simulation. The results show that compared with the traditional thermal network model, the improved thermal network model proposed in this paper can more comprehensively analyse the temperature field distribution and calculate the node temperature more accurately. [ABSTRACT FROM AUTHOR]