Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs

Sadeghi, S.; Jafari, Hossein; Nemati, Somayeh

doi:10.1016/j.chaos.2020.109736

Cited by 54 publications

(35 citation statements)

References 23 publications

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“…In this subsection, we present the error bound for the approximate ABC-derivative using an operational matrix based on poly-Bernoulli polynomials. The error bound basically follows the operational matrix using Genocchi polynomials as in [32].…”

Section: Error Boundmentioning

confidence: 99%

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

2020

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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.

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Section: Error Boundmentioning

confidence: 99%

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

2020

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“…A new technique for solving non-linear Volterra integro-differential equations in Atangana-Baleanu derivative sense has been introduced in [12] . Another technique with the uses of Genocchi polynomials has been proposed in [35] . A new technique to solve multi-variable order differential equations in AB sense has been introduced by Ganji et al.…”

Section: Introductionmentioning

confidence: 99%

Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives

Nabi

Abboubakar

Kumar

2020

Chaos, Solitons & Fractals

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In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of the citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold has been estimated to be  ∼ 3.41 as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 daily confirmed cases. The tally of cumulative infected cases could reach  ∼ 20, 100 cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations enlightened the fact that if the fractional order α is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0  < α <  1) leads to the delaying of the epidemic peaks.

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“…Orthogonal functions or polynomials, such as Haar wavelets [13], block-pulse functions (BPFs) [14], shifted Legendre polynomials [15] and Genocchi polynomials [16] have been widely adopted to handle different kinds of FDEs. Their foundation is to convert the FDE to a system of algebraic equations through an operational matrix, thus simplifying the problem.…”

Section: Introductionmentioning

confidence: 99%

Solving fractional differential equations using collocation method based onhybrid of block-pulse functions and Taylor polynomials

Lü¹,

Tang²

2021

Turk J Math

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In this paper, a novel approach is proposed to solve fractional differential equations (FDEs) based on hybrid functions. The hybrid functions consist of block-pulse functions and Taylor polynomials. The exact formula for the Riemann-Liouville fractional integral of the hybrid functions is derived via Laplace transform. The FDE under consideration is converted into an algebraic equation with undetermined coefficients by using this formula. A set of linear or nonlinear equations are obtained through collocating the algebraic equation at Newton-Cotes nodes. The numerical solution of the FDE is achieved by solving the linear or nonlinear equations. Error analysis is performed on the proposed method. Several numerical examples are given, and the results have proven that the proposed method is effective.

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Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs

Cited by 54 publications

References 23 publications

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

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

Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives

Solving fractional differential equations using collocation method based onhybrid of block-pulse functions and Taylor polynomials

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