A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions

2020 ◽  
Vol 141 ◽  
pp. 110282
Author(s):  
Sunil Kumar Sharma ◽  
Dinesh Kumar
Keyword(s):  
Fractional Order ◽  
Numerical Study ◽  
Legendre Functions ◽  
Fractional Model

Initialization of Identification of Fractional Model by Output-Error Technique

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Abir Khadhraoui ◽  
Khaled Jelassi ◽  
Jean-Claude Trigeassou ◽  
Pierre Melchior
Keyword(s):  
Numerical Simulation ◽  
Least Squares ◽  
Fractional Order ◽  
Fractional Integration ◽  
New Approach ◽  
Fractional Model ◽  
Output Error

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

scholarly journals A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021 ◽  
Vol 5 (3) ◽  
pp. 85
Author(s):  
Tayyaba Akram ◽  
Zeeshan Ali ◽  
Faranak Rabiei ◽  
Kamal Shah ◽  
Poom Kumam
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Numerical Study ◽  
Stability And Convergence ◽  
Weakly Singular Kernel ◽  
Integro Differential Equation ◽  
Suggested Technique ◽  
Collocation Approach ◽  
The Stability ◽  
Efficiency And Reliability

Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

scholarly journals Tau-Path Following Method for Solving the Riccati Equation with Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Muhammed I. Syam ◽  
Hani I. Siyyam ◽  
Ibrahim Al-Subaihi
Keyword(s):  
Fractional Derivative ◽  
Riccati Equation ◽  
Fractional Order ◽  
Path Following ◽  
Numerical Results ◽  
Legendre Functions ◽  
Path Following Methods

A formulation for the fractional Legendre functions is constructed to find the solution of the fractional Riccati equation. The fractional derivative is described in the Caputo sense. The method is based on the Tau Legendre and path following methods. Theoretical and numerical results are presented. Analysis for the presented method is given.

Sign in / Sign up

Export Citation Format

Share Document