scholarly journals A Taylor method for numerical solution of generalized pantograph equations with linear functional argument

2007 ◽  
Vol 200 (1) ◽  
pp. 217-225 ◽  
Author(s):  
Mehmet Sezer ◽  
Ayşegül Akyüz-Daşcıogˇlu
Keyword(s):  
Numerical Solution ◽  
Linear Functional ◽  
Taylor Method ◽  
Functional Argument

scholarly journals A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid K. Ali ◽  
Mohamed A. Abd El salam ◽  
Emad M. H. Mohamed
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Order ◽  
Linear Functional ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Fractional Order Differential Equations ◽  
The Given ◽  
Functional Argument ◽  
Special Case

AbstractIn this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

scholarly journals Spectral Tau method for solving general fractional order differential equations with linear functional argument

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Kamal R. Raslan ◽  
Mohamed A. Abd El salam ◽  
Khalid K. Ali ◽  
Emad M. Mohamed
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Linear Functional ◽  
Numerical Technique ◽  
Tau Method ◽  
Fractional Order Differential Equations ◽  
Functional Argument

Abstract In this paper, a numerical technique for solving new generalized fractional order differential equations with linear functional argument is presented. The spectral Tau method is extended to study this problem, where the derivatives are defined in the Caputo fractional sense. The proposed equation with its functional argument represents a general form of delay and advanced differential equations with fractional order derivatives. The obtained results show that the proposed method is very effective and convenient.

The Numerical Solution of the Bagley–Torvik Equation With Fractional Taylor Method

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
V. S. Krishnasamy ◽  
M. Razzaghi
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Vector Approximation ◽  
Taylor Method

In this paper, a numerical method for solving the fractional Bagley–Torvik equation is given. This method is based on using fractional Taylor vector approximation. The operational matrix of the fractional integration for fractional Taylor vector is given and is utilized to reduce the solution of the Bagley–Torvik equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.

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