scholarly journals A numerical method for finding solution of the distributed‐order time‐fractional forced Korteweg–de Vries equation including the Caputo fractional derivative

2021 ◽  
Author(s):  
Mohammad Hossein Derakhshan ◽  
Azim Aminataei
Keyword(s):  
Fractional Derivative ◽  
Numerical Method ◽  
Caputo Fractional Derivative ◽  
Vries Equation ◽  
De Vries ◽  
Distributed Order

scholarly journals Fractal complex transform technology for fractal Kkorteweg-de Vries equation within a local fractional derivative

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 841-845
Author(s):  
Jinze Xu ◽  
Zeng-Shun Chen ◽  
Jian-Hong Wang ◽  
Ping Cui ◽  
Yunru Bai
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Vries Equation ◽  
Special Functions ◽  
Traveling Wave Solutions ◽  
Cantor Sets ◽  
Local Fractional Derivative ◽  
Linear Partial Differential Equations ◽  
Wave Solutions ◽  
De Vries

In this paper, we present the fractal complex transform via a local fractional derivative. The traveling wave solutions for the fractal Korteweg-de Vries equations within local fractional derivative are obtained based on the special functions defined on Cantor sets. The technology is a powerful tool for solving the local fractional non-linear partial differential equations.

scholarly journals Approximate analytical solution for modified Korteweg-de Vries equation with local fractional derivative via new iterative method

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4027-4032
Author(s):  
Shu-Xian Deng ◽  
Zhi-Jun Wang
Keyword(s):  
Analytical Solution ◽  
Iterative Method ◽  
Fractional Derivative ◽  
Vries Equation ◽  
Approximate Analytical Solution ◽  
Variable Coefficients ◽  
Local Fractional Derivative ◽  
De Vries ◽  
New Iterative Method

In this paper, we obtain the approximate analytical solution of variable coefficients modified Korteweg-de Vries equation with local fractional derivative by using new iterative method.

scholarly journals A subinterval-based method for circuits with fractional order elements

2014 ◽  
Vol 62 (3) ◽  
pp. 449-454 ◽  
Author(s):  
M. Sowa
Keyword(s):  
Fractional Derivative ◽  
Numerical Method ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Polynomial Interpolation ◽  
Time Interval ◽  
Traditional Methods ◽  
Linear Circuit ◽  
Entire Time ◽  
Analytical Formulae

Abstract The paper deals with the solution of problems that concern fractional time derivatives. Specifically the author’s interest lies in solving circuit problems with so called fractional capacitors and fractional inductors. A numerical method is proposed that involves polynomial interpolation and the division of the entire time interval (for which computations are performed) into subintervals. Analytical formulae are derived for the integro-differentiation according to the Caputo fractional derivative. The rules that concern the subinterval dynamics throughout the computation are also presented in the paper. For exemplary linear circuit problems (AC and transient) involving fractional order elements the solutions have been obtained. These solutions are compared with ones obtained by means of traditional methods

Integration of the nonlinear modified Korteweg-de Vries equation with a loaded term

2020 ◽  
Vol 2020 (2) ◽  
pp. 85-98
Author(s):  
A.B. Khasanov ◽  
T.J. Allanazarova
Keyword(s):  
Vries Equation ◽  
De Vries ◽  
Loaded Term
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