NUMERICAL SOLUTION FOR A VARIABLE-ORDER FRACTIONAL NONLINEAR CABLE EQUATION VIA CHEBYSHEV CARDINAL FUNCTIONS, "Журнал вычислительной математики и математической физики"

2017 ◽  
pp. 2098
Author(s):  
Abdi-Mazraeh Somayeh ◽  
Irandoust-Pakchin Safar ◽  
Khani Ali
Keyword(s):  
Numerical Solution ◽  
Variable Order ◽  
Cable Equation ◽  
Cardinal Functions

Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

2021 ◽  
Author(s):  
C. J. Zúñiga-Aguilar ◽  
J. F. Gómez-Aguilar ◽  
H. M. Romero-Ugalde ◽  
R. F. Escobar-Jiménez ◽  
G. Fernández-Anaya ◽  
...  
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Differential Equations ◽  
Numerical Solution ◽  
Variable Order ◽  
Artificial Neural

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

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