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Semi-analytical scheme with its stability analysis for solving the fractional-order predator-prey equations by using Laplace-VIM

Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 4

5-17

EN

The article’s goal is to implement a semi-analytical technique named, the Laplace variational iteration method (LVIM), which is the combination of VIM and Laplace transform method. Although both the Laplace transform method and VIM cannot be applied to some nonlinear fractional differential equations (FDEs) individually, this combination will give a fast-convergent solution to the problem under study. The proposed scheme is used to numerically solve a biodynamic system called the Lotka-Volterra system, i.e. Predator-Prey Equations (PPEs). The system of FDEs can be used to represent this scenario, as well as the Caputo-Fabrizio fractional derivative will be used throughout the study. By assessing the residual error function, we can confirm that the given procedure is effective and accurate. The outcomes demonstrate that the technique used is an effective tool for simulating such models.

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Projekt rozpoznawania krawędzi w obrazie na podstawie algorytmów detekcji krawędzi

Kucharski Robert, Matuszewski Jan

Elektronika : konstrukcje, technologie, zastosowania

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2022

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Vol. 63, Nr 7

5--10

PL

W artykule przedstawiono aplikację komputerową opracowaną w środowisku programowym MATLAB do obliczania krawędzi w obrazie, wykorzystującą algorytmy detekcji krawędzi. Do stworzenia aplikacji wykorzystano obraz barwnego ptaka, w celu wyodrębnienia jak największej ilości krawędzi. Dla każdego algorytmu przedstawiony został histogram obrazu reprezentujący rozkład liczbowy występowania w obrazie różnych poziomów jasności. Wyniki obliczeń dały możliwość porównania algorytmów względem błędu średniokwadratowego (MSE) i stosunku sygnału do szumu (PSNR).

EN

The article presents a computer application developed in the MATLAB software environment to calculate edges in an image, using edge detection algorithms. The image of a colorful bird was used to create the application in order to extract as many edges as possible. For each algorithm, an image of histogram was presented representing the numerical distribution of the occurrence of different brightness levels in the image. The results of the calculations made it possible to compare the algorithms based on the mean square error (MSE) and the peak signal-to-noise ratio (PSNR).

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The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach

Maayah Banan, Moussaoui Asma, Bushnaq Samia, Arqub Omar Abu

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

963--977

EN

COVID-19, a novel coronavirus disease, is still causing concern all over the world. Recently, researchers have been concentrating their efforts on understanding the complex dynamics of this widespread illness. Mathematics plays a big role in understanding the mechanism of the spread of this disease by modeling it and trying to find approximate solutions. In this study, we implement a new technique for an approximation of the analytic series solution called the multistep Laplace optimized decomposition method for solving fractional nonlinear systems of ordinary differential equations. The proposed method is a combination of the multistep method, the Laplace transform, and the optimized decomposition method. To show the ability and effectiveness of this method, we chose the COVID-19 model to apply the proposed technique to it. To develop the model, the Caputo-type fractional-order derivative is employed. The suggested algorithm efficacy is assessed using the fourth-order Runge-Kutta method, and when compared to it, the results show that the proposed approach has a high level of accuracy. Several representative graphs are displayed and analyzed in two dimensions to show the growth and decay in the model concerning the fractional parameter α values. The central processing unit computational time cost in finding graphical results is utilized and tabulated. From a numerical viewpoint, the archived simulations and results justify that the proposed iterative algorithm is a straightforward and appropriate tool with computational efficiency for several coronavirus disease differential model solutions.