A computational algorithm for simulating fractional order relaxation–oscillation equation

SeMA Journal ◽  
2021 ◽  
Author(s):  
Mohammad Izadi
Keyword(s):  
Fractional Order ◽  
Computational Algorithm ◽  
Relaxation Oscillation ◽  
Oscillation Equation

Exact Analytical Solution of Fractional Relaxation-Oscillation Equation by Adomian Decomposition and He’s Variational Technique

2009 ◽  
Author(s):  
K. C. Basak ◽  
P. C. Ray ◽  
R. K. Bera
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Decomposition Method ◽  
Exact Analytical Solution ◽  
Relaxation Oscillation ◽  
Variational Technique ◽  
Adomian Decomposition ◽  
Fractional Relaxation ◽  
Oscillation Equation

Exact solution of linear fractional relaxation-oscillation equation is obtained by the decomposition method of Adomian and also by He’s variational method for fractional order α, for 1 < α ≤ 2. Surface plots of the above solution are drawn for different values of fractional order α and time t. Amplitude of the oscillation increases with α but it decreases as time increases.

Determination of the fractional order in semilinear subdiffusion equations

2020 ◽  
Vol 23 (3) ◽  
pp. 694-722
Author(s):  
Mykola Krasnoschok ◽  
Sergei Pereverzyev ◽  
Sergii V. Siryk ◽  
Nataliya Vasylyeva
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Computational Algorithm ◽  
Optimality Criterion ◽  
Small Time ◽  
Inverse Boundary ◽  
Regularization Scheme ◽  
Numerical Tests ◽  
With Memory

AbstractWe analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

scholarly journals Numerical approach for solving fractional relaxation–oscillation equation

2013 ◽  
Vol 37 (8) ◽  
pp. 5927-5937 ◽  
Author(s):  
Mustafa Gülsu ◽  
Yalçın Öztürk ◽  
Ayşe Anapalı
Keyword(s):  
Relaxation Oscillation ◽  
Numerical Approach ◽  
Fractional Relaxation ◽  
Oscillation Equation

scholarly journals Solving the Oscillation Equation With Fractional Order Damping Term Using a New Fourier Transform Method

2017 ◽  
Vol 13 (5) ◽  
pp. 7393-7397
Author(s):  
OZLEM OZTURK MIZRAK
Keyword(s):  
Fourier Transform ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Fourier Transformation ◽  
Cosmic Time ◽  
Damping Term ◽  
Fractional Damping ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Oscillation Equation

We propose an adapted Fourier transform method that gives the solution of an oscillation equation with a fractional damping term in ordinary domain. After we mention a transformation of cosmic time to individual time (CTIT), we explain how it can reduce the problem from fractional form to ordinary form when it is used with Fourier transformation, via an example for 1 < alpha < 2; where alpha is the order of fractional derivative. Then, we give an application of the results.

Generalized wavelet collocation method for solving fractional relaxation–oscillation equation arising in fluid mechanics

2017 ◽  
Vol 06 (02) ◽  
pp. 1750016
Author(s):  
Firdous A. Shah ◽  
R. Abass
Keyword(s):  
Fluid Mechanics ◽  
Relaxation Oscillation ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Specific Test ◽  
Fractional Relaxation ◽  
Oscillation Equation

In this paper, a generalized wavelet collocation operational matrix method based on Haar wavelets is proposed to solve fractional relaxation–oscillation equation arising in fluid mechanics. Contrary to wavelet operational methods accessible in the literature, we derive an explicit form for the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

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