A numerical method for solving fractional delay differential equations based on the operational matrix method

2021 ◽  
Vol 147 ◽  
pp. 110977
Author(s):  
Muhammed I. Syam ◽  
Mwaffag Sharadga ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Delay Differential Equations ◽  
Matrix Method ◽  
Operational Matrix ◽  
Operational Matrix Method ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

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.

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

2021 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
İbrahim Avcı 
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

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