THE FRACTIONAL LAPLACE TRANSFORM SOLUTION FOR FRACTIONAL DIFFERENTIAL EQUATION THE OSCILLATOR IN THE PRESENCE OF AN EXTERNAL FORCES

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Choksi Hetal
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Harmonic Oscillator ◽  
Fractional Differential Equation ◽  
Driving Force ◽  
Resisting Medium ◽  
Fractional Differential ◽  
The Given ◽  
Potential Tool ◽  
External Driving

The Fractional Laplace transform is applied to derive the solution of fractional differential equation of order governing the motion of the Harmonic Oscillator in a Non-Resisting Medium. The Fractional Laplacetransform method is to provide a potential tool to solve such a type of Fractional differential equation. Further consider oscillator in the presence of an external driving force of is in the fractional form and investigate some interesting features of the given equation. Also discuss the Numerical form of the oscillator in a r. The Fractional Laplace transform is applied to derive the solution of fractional differential equation of order governing the motion of the Harmonic Oscillator in a Non-Resisting Medium. The Fractional Laplacetransform method is to provide a potential tool to solve such a type of Fractional differential equation. Further consider oscillator in the presence of an external driving force of is in the fractional form and investigate some interesting features of the given equation. Also discuss the Numerical form of the oscillator in a resisting medium and discuss some cases of oscillation fractional differential equations for external driving force. esisting medium and discuss some cases of oscillation fractional differential equations for external driving force.

Two dimensional fractional projectile motion in a resisting medium

Open Physics ◽  
2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Juan Rosales ◽  
Manuel Guía ◽  
Francisco Gómez ◽  
Flor Aguilar ◽  
Juan Martínez
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Two Dimensional ◽  
Auxiliary Parameter ◽  
Derivative Operator ◽  
Projectile Motion ◽  
Resisting Medium ◽  
Fractional Differential ◽  
The Given ◽  
Physical Quantities

AbstractIn this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)−1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.

scholarly journals Analytic Solution for theRLElectric Circuit Model in Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
P. V. Shah ◽  
A. D. Patel ◽  
I. A. Salehbhai ◽  
A. K. Shukla
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Analytic Solution ◽  
Electrical Circuit ◽  
Special Cases ◽  
The Laplace Transform ◽  
Fractional Differential

This paper provides an analytic solution ofRLelectrical circuit described by a fractional differential equation of the order0<α≤1. We use the Laplace transform of the fractional derivative in the Caputo sense. Some special cases for the different source terms have also been discussed.

scholarly journals Solution of an extraordinary differential equation by Adomian decomposition method

2004 ◽  
Vol 2004 (4) ◽  
pp. 331-338 ◽  
Author(s):  
S. Saha Ray ◽  
R. K. Bera
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Fractional Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Alternative Method ◽  
Adomian Decomposition ◽  
Fractional Differential

The aim of the present analysis is to apply the Adomian decomposition method for the solution of a fractional differential equation as an alternative method of Laplace transform.

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