On construction of solutions of linear fractional differential equations with constant coefficients

2016 ◽  
Author(s):  
Meiirkhan B. Borikhanov ◽  
Batirkhan Kh. Turmetov
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Constant Coefficients ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

scholarly journals On the solution of some simple fractional differential equations

1990 ◽  
Vol 13 (3) ◽  
pp. 481-496 ◽  
Author(s):  
L. M. B. C. Campos
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Power Type ◽  
Integer Order ◽  
Constant Coefficients ◽  
Fractional Differential ◽  
Exponential Power ◽  
Derivatives Of ◽  
Linear Fractional Differential Equations

The differintegration or fractional derivative of complex orderν, is a generalization of the ordinary concept of derivative of ordern, from positive integerν=nto complex values ofν, including also, forν=−na negative integer, the ordinaryn-th primitive. Substituting, in an ordinary differential equation, derivatives of integer order by derivatives of non-integer order, leads to a fractional differential equation, which is generallyaintegro-differential equation. We present simple methods of solution of some classes of fractional differential equations, namely those with constant coefficients (standard I) and those with power type coefficients with exponents equal to the orders of differintegration (standard II). The fractional differential equations of standard I (II), both homogeneous, and inhomogeneous with exponential (power-type) forcing, can be solved in the ‘Liouville’ (‘Riemann’) systems of differintegration. The standard I (II) is linear with constant (non-constant) coefficients, and some results are also given for a class of non-linear fractional differential equations (standard III).

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.

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