1,721,021 research outputs found
Homotopy perturbation method for solving a three-species food chain model
No full textIn this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equa tion systems such as a three-species food chain model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. Some plots are presented to show the reliability and simplicity of the methods
A new approach to solving local fractional Riccati differential equations using the Adomian-Elzaki method
No full textThe Elzaki-Adomian decomposition method (EADM) is intended to serve as an efficient analytical method for the resolution of these original fractional-order Riccati differential equations. This can be accomplished permanently by incorporating the Adomian decomposition method with Elzaki. The local fractional derivative is implemented in this format. Particularly in the context of nonlinear differential equations (ODE), this approach is preferred over digital gaps. Additionally, the method’s convergence. Random individuals with uniform, beta, normal, and gamma distributions are used to select the initial conditions or coefficients of the equations. The variance, confidence interval, and expected value of the solutions that are obtained will be determined. MATLAB (2013a) package software will be employed to display the individuals that were brought together, and the results will be analyzed randomly. © 2025 the Author(s), licensee AIMS Press
Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method
No full textIn this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge–Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.2-s2.0-7995330807
Investigation of fractional order covid-19 model with q-homotopy analysis transform method
No full textThe primary objective of this paper is to derive approximate analytic solutions for the time fractional-order Covid-19 model by employing the q-homotopy analysis transform method (q-HATM) and the Laplace transform homotopy perturbation method (LT-HPM). The covid 19 model is a system of five-dimensional nonlinear ordinary differential equations. Moreover, this method applies even to more complex partial differential equations originating from mathematical biology, demonstrating computational efficiency and wide application. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied to analyze the approximate solutions of the system. Graphical results are presented and discussed quantitatively to illustrate the approximate solution. Copyright 2021, Yıldız Technical University
DYNAMICAL ANALYSIS OF THE CONFORMABLE FRACTIONAL ORDER HOST-PARASITE MODEL
No full textIn this study, the differential equation system with a mathematical model of parasites is examined in cases where infection does not depend on transmission and defense, but on the level of infectivity and defense of the parasite and host. When discretization is applied to the differential equation, a two-dimensional discrete system is obtained in the range of t is an element of [n, n + 1] then the stability of the Neimark-Sacker bifurcation of the positive equilibrium point of this discrete system is investigated. Finally, MAPLE and MATLAB package program are used to show the accuracy of the results obtained.WOS:000817811400004Q
On solutions of time fractional order random HIV/AIDS modelling
No full textIn this study, The fractional random HIV/AIDS model approximate analytical solutions were produced using the differential transformation method. The approximate analytical solution of the fractional order Random HIV/AIDS model was obtained with the help of the differential transformation method. For the fractional random HIV/AIDS model, which was created by choosing the initial conditions from the exponential, beta, and normal distributions, graphic simulations of the expected value, variance, and confidence intervals of the most commonly used probability characteristics were obtained with the help of the MATLAB package program. Results obtained are interpreted. © 2024 Yildiz Technical University. All rights reserved
Analysis of Random Difference Equations Using the Differential Transformation Method
No full textThe differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. In this study, we apply the theorems related to the DTM to the given examples and investigate the behaviour of the approximate analytical solutions. The expected value, variance, coefficient of variation, and confidence intervals of the solutions of random difference equations obtained from discrete probability distributions such as uniform, geometric, Poisson, and binomial distributions will be calculated. Maple and MATLAB software packages are used to plot the solution graphs and also to interpret the solution behaviour. © 2024 Şeyma Şişman and Mehmet Merdan
1 of 1 Analysis of a discrete time fractional-order Vallis system
No full textVallis system is a model describing nonlinear interactions of the atmosphere and temperature fluctuations with a strong influence in the equatorial part of the Pacific Ocean. As the model approaches the fractional order from the integer order, numerical simulations for different situations arise. To see the behavior of the simulations, several cases involving integer analysis with different non-integer values of the Vallis systems were applied. In this work, a fractional mathematical model is constructed using the Caputo derivative. The local asymptotic stability of the equilibrium points of the fractional-order model is obtained from the fundamental production number. The chaotic behavior of this system is studied using the Caputo derivative and Lyapunov stability theory. Hopf bifurcation is used to vary the oscillation of the system in steady and unsteady states. In order to perform these numerical simulations, we apply Grunwald-Letnikov tactics with Binomial coefficients to obtain the effects on the non-integer fractional degree and discrete time vallis system and plot the phase diagrams and phase portraits with the help of MATLAB and MAPLE packages.WOS:001135946200001Q
An approximate solution of a model for HIV infection of CD4+ T cells
No full textIn this paper, the approximate solution of the differential system modeling HIV infection of CD4+ T cells is obtained by a reliable algorithm based on an adaptation of the standard variational iteration method (VIM), which is called the multi-stage variational iteration method(MSVIM). A comparison between MSVIM and the fourthorder Runge-Kutta method (RK4-method) reveal that the proposed technique is a promising tool to solve the considered problem.2-s2.0-8005152434
On the solution of random linear difference equations with Laplace transform method
No full textIn this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete-time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program. © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd
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