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Open AccessArticle

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

1
Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Campus Pagoh, Pagoh 84600, Malaysia
2
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Campus Segamat, Segamat 85000, Malaysia
*
Author to whom correspondence should be addressed.
Computation 2020, 8(3), 82; https://doi.org/10.3390/computation8030082
Received: 9 August 2020 / Revised: 12 September 2020 / Accepted: 14 September 2020 / Published: 16 September 2020
(This article belongs to the Section Computational Engineering)
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. View Full-Text
Keywords: poly-Bernoulli polynomials; operational matrix; delay operational matrix; fractional delay differential equations poly-Bernoulli polynomials; operational matrix; delay operational matrix; fractional delay differential equations
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MDPI and ACS Style

Phang, C.; Toh, Y.T.; Md Nasrudin, F.S. An Operational Matrix Method Based on Poly-Bernoulli Polynomials for Solving Fractional Delay Differential Equations. Computation 2020, 8, 82.

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