Solving partial fractional differential equations by using the Laguerre wavelet-Adomian method

By using a nonlinear method, we try to solve partial fractional differential equations. In this way, we construct the Laguerre wavelets operational matrix of fractional integration. The method is proposed by utilizing Laguerre wavelets in conjunction with the Adomian decomposition method. We present the procedure of implementation and convergence analysis for the method. This method is tested on fractional Fisher’s equation and the singular fractional Emden–Fowler equation. We compare the results produced by the present method with some well-known results.

Image Compression Based with Multi Discrete Laguerre Wavelets Transform

The colored image has a large array of numbers that take up a lot of space, creating a problem with transportation and storage, which needs to be urgently solved. It’s essential to find a mathematical tool that shrinks this space when transferring and storing the colored image over the years. Continuous waves such as Fourier and discrete waves such as Haar Symlet 2, coiflet 2, and daubecheis 2 were founded by shrinkage and expansion and characterized with the help of s and r parameters. With the help of the MATLAB program, these basic wavelets installed supplication and image compression, analysis, and lifting procedures. In this study, new waves based on polynomials were discovered, relying on the parent function and through many calculations, clarifying many theories and important features that this wave possesses, such as the orthogonal feature and approach that qualifies these new waves in image processing such as squeeze, jam, and analyze images by searching for a filter. It is suitable and new for carrying out the analysis and reconstruction process with high-pass and low-pass filters resulting from the scaling and wavelet function. Four samples of color images are shown. The compression process was carried out with the help of MATLAB. The use of new waves is Multi Discrete Laguerre Wavelet Transfer, where the standard criteria resulting from the compression process were calculated and the most efficient results were obtained without losing the original information of the image, compared to the standard waves’ tables, which will demonstrate the efficiency of these new wavelets in Multi Discrete Laguerre Wavelet transform.