Solving Linear Fractional Differential Equations with Time Delay by Steps Chebyshev-Tau Scheme

2021 ◽  
Author(s):  
M. Mousa-Abadian ◽  
S. H. Momeni-Masuleh
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

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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