scholarly journals Modified spline collocation for linear fractional differential equations

2015 ◽  
Vol 283 ◽  
pp. 28-40 ◽  
Author(s):  
Marek Kolk ◽  
Arvet Pedas ◽  
Enn Tamme
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Spline Collocation ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

Numerical solution of fractional differential equations by using fractional B-spline

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Hossein Jafari ◽  
Chaudry Khalique ◽  
Mohammad Ramezani ◽  
Haleh Tajadodi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Spline Collocation ◽  
B Spline ◽  
Computational Work ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

AbstractIn this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.

Systems of Nonlinear Fractional Differential Equations

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Right ◽  
Linear Fractional Differential Equations

AbstractUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives $D^{q}_{T}x$ and $D^{q}_{T}y$. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

The Solution of Linear Fractional Differential Equations Using the Fractional Meta-Trigonometric Functions

2011 ◽  
Author(s):  
Carl F. Lorenzo ◽  
Rachid Malti ◽  
Tom T. Hartley
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Laplace Transforms ◽  
New Method ◽  
Trigonometric Functions ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.

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