scholarly journals COMPARISON OF TWO NUMERICAL METHODS FOR FRACTIONAL-ORDER RӦSSLER SYSTEM

2020 ◽  
pp. 53-60
Author(s):  
Ylldrita Seferi
Keyword(s):  
Numerical Methods ◽  
Fractional Order

scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

A numerical framework for the approximate solution of fractional tumor-obesity model

2019 ◽  
Vol 10 (01) ◽  
pp. 1941008 ◽  
Author(s):  
Sadia Arshad ◽  
Dumitru Baleanu ◽  
Ozlem Defterli ◽  
Shumaila
Keyword(s):  
Immune Response ◽  
Approximate Solution ◽  
Numerical Methods ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Response Rate ◽  
Stability And Convergence ◽  
Fractional Operators ◽  
High Caloric Diet

In this paper, we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and Caputo-Fabrizio (CF). Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed. Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models. We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.

Fractional Order Generalized Electro-Magneto-Thermo-Elasticity with Magnetic Monopoles and Geometrical Nonlinearity

2013 ◽  
Vol 273 ◽  
pp. 162-166 ◽  
Author(s):  
Ya Jun Yu ◽  
Xiao Geng Tian
Keyword(s):  
Electromagnetic Field ◽  
Numerical Methods ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Inverse Method ◽  
Geometrical Nonlinearity ◽  
Generalized Thermoelasticity ◽  
Magnetic Monopoles ◽  
Rate Dependent ◽  
Temperature Rate

Recently, Youssef developed the fractional order generalized thermoelasticity (FOGTE) in the context of extended thermoelasticity (ETE). In this work, we extended the concept of fractional calculus into the temperature rate dependent thermoelasticity (TRDTE) and introduced the unified form of the two cases. Upon introducing the electromagnetic field with magnetic monopoles and considering the geometrical nonlinearity, we proposed a fractional order generalized electro-magneto- thermo-elasticity (FOGEMm-poleTEg-non) with magnetic monopoles (m-pole) and geometrical nonlinearity (g-non). To deal with multi-physics problems using numerical methods, we obtained a generalized variational theorem by using the semi-inverse method.

scholarly journals Two numerical methods for Abel's integral equation with comparison

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Abdallah Ali Badr
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Fractional Order ◽  
Quadrature Formula ◽  
Approximate Formula ◽  
Simple Pole ◽  
Numerical Examples ◽  
International Audience ◽  
Modified Formula

International audience Analogy between Abel's integral equation and the integral of fractional order of a given function, j^α f(t), is discussed. Two different numerical methods are presented and an approximate formula for j^α f(t) is obtained. The first approach considers the case when the function, f(t), is smooth and a quadrature formula is obtained. A modified formula is deduced in case the function has one or more simple pole. In the second approach, a procedure is presented to weaken the singularities. Both two approaches could be used to solve numerically Abel's integral equation. Some numerical examples are given to illustrate our results.

scholarly journals A Collocation Method for the Numerical Solution of Nonlinear Fractional Dynamical Systems

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 156 ◽  
Author(s):  
Francesca Pitolli
Keyword(s):  
Applied Sciences ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Order ◽  
Time Derivative ◽  
Test Problems ◽  
Fractional Differential

Fractional differential problems are widely used in applied sciences. For this reason, there is a great interest in the construction of efficient numerical methods to approximate their solution. The aim of this paper is to describe in detail a collocation method suitable to approximate the solution of dynamical systems with time derivative of fractional order. We will highlight all the steps necessary to implement the corresponding algorithm and we will use it to solve some test problems. Two Mathematica Notebooks that can be used to solve these test problems are provided.

Comparing Two Numerical Methods for Approximating a New Giving Up Smoking Model Involving Fractional Order Derivatives

2017 ◽  
Vol 41 (3) ◽  
pp. 569-575 ◽  
Author(s):  
Vedat Suat Erturk ◽  
Gul Zaman ◽  
Baha Alzalg ◽  
Anwar Zeb ◽  
Shaher Momani
Keyword(s):  
Numerical Methods ◽  
Fractional Order

scholarly journals Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xiaoli Qiang ◽  
Kamran ◽  
Abid Mahboob ◽  
Yu-Ming Chu
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Fractional Order ◽  
Integrodifferential Equations ◽  
Inverse Laplace Transform ◽  
Laplace Domain ◽  
The Real ◽  
Volterra Integrodifferential Equation ◽  
Engineering Sciences ◽  
Real Domain

Laplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to the real domain by analytic methods. Therefore, we need numerical methods to invert the solution to the real domain. In this work, we construct numerical schemes based on Laplace transform for the solution of fractional-order Volterra integrodifferential equations in the sense of the Atangana-Baleanu Caputo derivative. We propose two numerical methods for approximating the solution of fractional-order linear and nonlinear Volterra integrodifferential equations. In our scheme, the inverse Laplace transform is approximated using a contour integration method and Stehfest method. Some numerical experiments are performed to check the accuracy and efficiency of the methods. The results obtained using these methods are compared.

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