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.

LYAPUNOV-TYPE INEQUALITIES FOR LOCAL FRACTIONAL DIFFERENTIAL SYSTEMS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050131
Author(s):  
YONGFANG QI ◽  
LIANGSONG LI ◽  
XUHUAN WANG
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Systematic Design ◽  
Differential Systems ◽  
Design Algorithm ◽  
Fractional Differential Systems ◽  
Lyapunov Inequalities ◽  
Fractional Differential

This paper deals with the problem of Lyapunov inequalities for local fractional differential equations with boundary conditions. By using analytical method, a novel Lyapunov-type inequalities for the local fractional differential equations is provided. A systematic design algorithm is developed for the construction of Lyapunov inequalities.

scholarly journals Solving fractional circuits with sinusoidal sources by using the gcdAlpha method

2018 ◽  
Vol 19 ◽  
pp. 01008
Author(s):  
Marcin Sowa
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Fractional Differential

This paper concerns a study being part of a larger project aiming at solutions of problems with fractional time derivatives. The presented study concerns gcdAlpha – a semi-analytical method for solving fractional differential equations. The basis of the method is recalled along with the general form of problems it was designed to solve. Sources represented by sinusoidal time functions are considered and the general formulae for gcdAlpha are presented for this case. An exemplary circuit problem (containing fractional elements and a sinusoidal source) has been brought forward and solved. The results are compared with ones obtained through a solver basing on the numerical method called SubIval.

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 The Cădariu-Radu Method for Existence, Uniqueness and Gauss Hypergeometric Stability of Ω-Hilfer Fractional Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1408
Author(s):  
Safoura Rezaei Aderyani ◽  
Reza Saadati ◽  
Michal Fec̆kan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Unbounded Domains ◽  
Fractional Differential ◽  
Fractional System

Using the Cădariu–Radu method derived from the Diaz–Margolis theorem, we study the existence, uniqueness and Gauss hypergeometric stability of Ω-Hilfer fractional differential equations defined on compact domains. Next, we show the main results for unbounded domains. To illustrate the main result for a fractional system, we present an example.

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