A New Approach for an Analytical Solution for a System of Multi-term Linear Fractional Differential Equations

2021 ◽  
Author(s):  
Song-Guk Jong ◽  
Hui-Chol Choe ◽  
Yong-Do Ri
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
New Approach ◽  
Term Linear ◽  
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.

scholarly journals The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
W. K. Zahra ◽  
S. M. Elkholy
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Spline Function ◽  
Shooting Method ◽  
Polynomial Spline ◽  
Cubic Polynomial ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented.

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