scholarly journals Hermite Wavelet Method for Fractional Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Method Of Steps ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

We proposed a method by utilizing method of steps and Hermite wavelet method, for solving the fractional delay differential equations. This technique first converts the fractional delay differential equation to a fractional nondelay differential equation and then applies the Hermite wavelet method on the obtained fractional nondelay differential equation to find the solution. Several numerical examples are solved to show the applicability of the proposed method.

Dependence Analysis of the Solutions on the Parameters of Fractional Delay Differential Equations

2011 ◽  
Vol 3 (5) ◽  
pp. 586-597 ◽  
Author(s):  
Shuiping Yang ◽  
Aiguo Xiao ◽  
Xinyuan Pan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Initial Function ◽  
Hand Function ◽  
Dependence Analysis ◽  
Numerical Examples ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations ◽  
Theoretical Results

AbstractIn this paper, we investigate the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional delay differential equations (FDDEs) with the Caputo fractional derivative. Some results including an estimate of the solutions of FDDEs are given respectively. Theoretical results are verified by some numerical examples.

scholarly journals An Operational Matrix Method Based on Poly-Bernoulli Polynomials for Solving Fractional Delay Differential Equations

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 82
Author(s):  
Chang Phang ◽  
Yoke Teng Toh ◽  
Farah Suraya Md Nasrudin
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Operational Matrix ◽  
Bernoulli Polynomials ◽  
Variable Coefficients ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function. We first show some new properties for these poly-Bernoulli polynomials; then we derive new operational matrix based on poly-Bernoulli polynomials for the Atangana–Baleanu derivative. A delay operational matrix based on poly-Bernoulli polynomials is derived. The error bound of this new method is shown. We applied this poly-Bernoulli operational matrix for solving fractional delay differential equations with variable coefficients. The numerical examples show that this method is easy to use and yet able to give accurate results.

scholarly journals The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
M. M. Khader
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Approximate Formula ◽  
Laguerre Polynomials ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Generalized Laguerre Polynomials ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

scholarly journals Stability of scalar nonlinear fractional differential equations with linearly dominated delay

2020 ◽  
Vol 23 (1) ◽  
pp. 250-267 ◽  
Author(s):  
Hoang The Tuan ◽  
Stefan Siegmund
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Equilibrium Points ◽  
Asymptotic Behavior Of Solutions ◽  
Asymptotically Stable ◽  
Fractional Delay ◽  
Fractional Differential ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

AbstractIn this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay equation is asymptotically stable and show that the asymptotic stability of the trivial solution is preserved under a small nonlinear Lipschitz perturbation of the fractional delay differential equation.

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