ANALYTICAL SOLUTION FOR SOME SYSTEMS OF NONLINEAR CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS

2018 ◽  
Vol 109 (2) ◽  
pp. 243-259 ◽  
Author(s):  
Maher Jneid ◽  
Abdallah El Chakik
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential

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.

scholarly journals A new approximate analytical method for a system of fractional differential equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 853-858 ◽  
Author(s):  
Shao-Wen Yao ◽  
Kang-Le Wang
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Approximate Analytical Solution ◽  
Approximate Analytical Method ◽  
Fractional Differential ◽  
Fractional System

In this paper, a new approximate analytical method is established, and it is useful in constructing approximate analytical solution a system of fractional differential equations. The results show that our method is reliable and efficient for solving the fractional system.

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