scholarly journals Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial

2021 ◽  
Vol 5 (2) ◽  
pp. 64-68
Author(s):  
Salim S. Mahmood ◽  
Kamaran J. Hamad ◽  
‎Milad A. Kareem ◽  
Asrin F. Shex
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear Equation ◽  
Fractional Differential Equation ◽  
Legendre Polynomial ◽  
Conformable Derivative ◽  
Approximation Solution ◽  
Non Linear Equation ◽  
Non Linear ◽  
Fractional Differential

The aim of this article is the way for finding approximation solution of multi-order fractional differential equation with conformable sense with use approximated function by shifted Legendre polynomial, the method is easy and powerful for get our results of the linear and non-linear equation, the background idea behind this method is finding system of algebra after achieving messing variable is that mean obtain approximate solution, a few examples illustrates for presented how much our method is capable.

scholarly journals Ulam-Hyers Stability for Cauchy Fractional Differential Equation in the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Unit Disk ◽  
Fractional Differential Equations ◽  
Fractional Operators ◽  
Owa Operators ◽  
Non Linear ◽  
Fractional Differential

We prove the Ulam-Hyers stability of Cauchy fractional differential equations in the unit disk for the linear and non-linear cases. The fractional operators are taken in sense of Srivastava-Owa operators.

scholarly journals DGJ Method for Linear and Nonlinear Third order Fractional Differential Equation

2018 ◽  
Author(s):  
Mahmut Modanli
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Fractional Differential Equation ◽  
Initial Boundary ◽  
Third Order ◽  
Partial Differential ◽  
Approximation Solution ◽  
The Third ◽  
Numerical Result ◽  
Fractional Differential

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Simple Identification of Fractional Differential Equation

2011 ◽  
Vol 180 ◽  
pp. 331-338 ◽  
Author(s):  
Wojciech Mitkowski ◽  
Anna Obrączka
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Numerical Experiments ◽  
Identification Problem ◽  
Marquardt Algorithm ◽  
Non Linear ◽  
Fractional Differential ◽  
Estimation Parameters

In this paper the simple identification problem for fractional differential equation of Caputo type was considered. This is the problem of estimation parameters, for which the quadratic criterion is minimized. For solving this issue, the Non Linear Programing technique, based on Marquardt algorithm, was used. At the end of article the results for numerical experiments was presented.

scholarly journals Frenet frame with respect to conformable derivative

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1541-1550
Author(s):  
Uğur Gözütok ◽  
Hüsnü Çoban ◽  
Yasemin Sağıroğlu
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fundamental Theorem ◽  
Geometric Interpretation ◽  
Frenet Frame ◽  
Conformable Fractional Derivative ◽  
Conformable Derivative ◽  
Fractional Differential ◽  
Curvature And Torsion

Conformable fractional derivative is introduced by the authors Khalil at al in 2014. In this study, we investigate the frenet frame with respect to conformable fractional derivative. Curvature and torsion of a conformable curve are defined and the geometric interpretation of these two functions is studied. Also, fundamental theorem of curves is expressed for the conformable curves and an example of the curve corresponding to a fractional differential equation is given.

4. On the Linear Differential Equation of the Second Order

1878 ◽  
Vol 9 ◽  
pp. 93-98 ◽  
Author(s):  
Tait
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Arbitrary Constant ◽  
Second Order ◽  
General Linear ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

Design and Analysis of an oil Cushion

1973 ◽  
Vol 15 (1) ◽  
pp. 48-52 ◽  
Author(s):  
M. A. Satter
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Dynamic Characteristics ◽  
Order Linear Differential Equation ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential ◽  
Good Agreement

The dynamic characteristics of an oil cushion, which was originally designed to eliminate impactive excitation to a mechanical lever and thereby achieve noise reduction, have been studied both theoretically and experimentally. The system motion is represented by a second order non-linear differential equation which can be reduced to a first order linear differential equation by changing the variables. An approximate but simple solution to the non-linear equation has also been presented. Theoretical and experimental results have good agreement.

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