scholarly journals An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
M. R. Balooch Shahriyar ◽  
F. Ismail ◽  
S. Aghabeigi ◽  
A. Ahmadian ◽  
S. Salahshour
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
New Method ◽  
Fractional Differential ◽  
Fuzzy Fractional Differential Equations

A new method is proposed for solving systems of fuzzy fractional differential equations (SFFDEs) with fuzzy initial conditions involving fuzzy Caputo differentiability. For this purpose, three cases are introduced based on the eigenvalue-eigenvector approach; then it is shown that the solution of system of fuzzy fractional differential equations is vector of fuzzy-valued functions. Then the method is validated by solving several examples.

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.

scholarly journals Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. H. Heydari ◽  
M. R. Hooshmandasl ◽  
F. M. Maalek Ghaini ◽  
F. Mohammadi
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
General Procedure ◽  
Wavelet Expansion ◽  
Operational Matrices ◽  
Chebyshev Wavelets ◽  
Block Pulse Functions ◽  
Fractional Differential

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.

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