Fractional Newtonian mechanics

Abstract:In 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 was introduced in the derivative operator. This parameter has a dimension of inverse of seconds ( ) −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 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.

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“…in formulas (14) and (16) (14) and (16) value into equation (14). The time T is found by finding = T , when = 0.…”

Section: Fractional Two Dimensional Motionmentioning

confidence: 99%

Two dimensional fractional projectile motion in a resisting medium

et al. 2014

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“…However, the interested reader can see [5,7] for an alternative and interesting approach which is named "terminal value problems". Various applications of such problems imply a substantial demand for efficient schemes for their numerical handling [3,4,6,10,12]. Since few of the fractional differential equations encountered in practice can be solved explicitly, it is necessary to employ numerical techniques to find the approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional differential equations via a Volterra integral equation approach

Esmaeili¹,

Shamsi²,

Dehghan³

2013

Open Physics

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Abstract:The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.PACS (

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“…In consequence, the subject of fractional differential equations is gaining much importance and attention. For examples and details, see [1,2,3,4,5,6,7,8,9,10,11] and the references therein. However, the theory of boundary value problems for nonlinear fractional differential equations is still in the initial stages and many aspects of this theory need to be explored.…”

Section: Introductionmentioning

confidence: 99%

On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

Babakhani¹

2012

Journal of Nonlinear Analysis and Application

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Fractional Newtonian mechanics

Cited by 51 publications

References 40 publications

Two dimensional fractional projectile motion in a resisting medium

Two dimensional fractional projectile motion in a resisting medium

Numerical solution of fractional differential equations via a Volterra integral equation approach

On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

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