Numerical and Analytical Method for Solution of Fractional Differential Equations

2019 ◽  
Author(s):  
Pankaj Ramani ◽  
A. M. Khan ◽  
D. L. Suthar
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Fractional Differential

LYAPUNOV-TYPE INEQUALITIES FOR LOCAL FRACTIONAL DIFFERENTIAL SYSTEMS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050131
Author(s):  
YONGFANG QI ◽  
LIANGSONG LI ◽  
XUHUAN WANG
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Systematic Design ◽  
Differential Systems ◽  
Design Algorithm ◽  
Fractional Differential Systems ◽  
Lyapunov Inequalities ◽  
Fractional Differential

This paper deals with the problem of Lyapunov inequalities for local fractional differential equations with boundary conditions. By using analytical method, a novel Lyapunov-type inequalities for the local fractional differential equations is provided. A systematic design algorithm is developed for the construction of Lyapunov inequalities.

scholarly journals Solving fractional circuits with sinusoidal sources by using the gcdAlpha method

2018 ◽  
Vol 19 ◽  
pp. 01008
Author(s):  
Marcin Sowa
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Fractional Differential

This paper concerns a study being part of a larger project aiming at solutions of problems with fractional time derivatives. The presented study concerns gcdAlpha – a semi-analytical method for solving fractional differential equations. The basis of the method is recalled along with the general form of problems it was designed to solve. Sources represented by sinusoidal time functions are considered and the general formulae for gcdAlpha are presented for this case. An exemplary circuit problem (containing fractional elements and a sinusoidal source) has been brought forward and solved. The results are compared with ones obtained through a solver basing on the numerical method called SubIval.

scholarly journals Analysis of fractional duffing oscillator

2020 ◽  
Vol 66 (2 Mar-Apr) ◽  
pp. 187 ◽  
Author(s):  
S.C. Eze
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Duffing Oscillator ◽  
Laplace Method ◽  
Nonlinear Fractional Differential Equations ◽  
Non Linear ◽  
Fractional Differential

In this contribution, a simple analytical method (which is an elegant combination of a well known methods; perturbation method and Laplace method) for solving non-linear and non-homogeneous fractional differential equations is pro- posed. In particular, the proposed method was used to analysed the fractional Duffing oscillator.The technique employed in this method can be used to analyse other nonlinear fractional differential equations, and can also be extended to non- linear partial fractional differential equations.The performance of this method is reliable, effective and gives more general solution.

scholarly journals A new approximate analytical method for a system of fractional differential equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 853-858 ◽  
Author(s):  
Shao-Wen Yao ◽  
Kang-Le Wang
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Approximate Analytical Solution ◽  
Approximate Analytical Method ◽  
Fractional Differential ◽  
Fractional System

In this paper, a new approximate analytical method is established, and it is useful in constructing approximate analytical solution a system of fractional differential equations. The results show that our method is reliable and efficient for solving the fractional system.

scholarly journals Analytical solutions for conformable fractional Bratu-type equations

2018 ◽  
Vol 7 (1) ◽  
pp. 15 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Conformable Fractional Derivative ◽  
Fractional Differential

Solving fractional differential equations have a prominent function in different science such as physics and engineering. Therefore, are different definitions of the fractional derivative presented in recent years. The aim of the current paper is to solve the fractional differential equation by a semi-analytical method based on conformable fractional derivative. Fractional Bratu-type equations have been solved by the method and to show its capabilities. The obtained results have been compared with the exact solution.

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

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