Solution to the fractional logistic equation by modified Eulerian numbers

Kaharuddin, Liyana Nadhira; Phang, Chang; Jamaian, Siti Suhana

doi:10.1140/epjp/s13360-020-00135-y

Cited by 20 publications

(9 citation statements)

References 13 publications

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“…The logistic differential equation has many applications in different fields [1]. Recently, the fractional version of the logistic equation has been considered by many authors [2][3][4][5][6][7]. Very recently, some particular cases of the fractional logistic equation with power law coefficients have been solved [8].…”

Section: Introductionmentioning

confidence: 99%

Power series solution of the fractional logistic equation

Area

Nieto

2021

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

Power series solution of the fractional logistic equation

Area

Nieto

2021

Physica A: Statistical Mechanics and its Applications

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“…Consequently, exploring an approximate or numerical technique is of primary interest for such fractional equations. Therefore, there are several approximate techniques are used to solve fractional logistic equation, for instance, predictor-corrector approaches, 30 the finite difference schemes, 31 the spectral methods, 32,33 the Bessel collocation method, 34 modified Eulerian numbers, 35 and the Laguerre collocation method. 36 The "total metabolism" or aggregate sum of toxin delivered from the time t = 0 is determined by the integral term showing up in (2.3).…”

Section: Formulation Of the Fractional Volterra's Population Modelmentioning

confidence: 99%

Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system

Shah

Irfan

Nisar

2021

Math Methods in App Sciences

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In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones.

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“…n k is the k th polylogarithm function. Recently, this polylogarithm function has been widely used in deriving new polynomials or number sequences such as in [31]. For x = 0, we obtain the poly-Bernoulli numbers, b n (x) are as follows:…”

Section: The Properties Of Poly-bernoulli Polynomialsmentioning

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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Solution to the fractional logistic equation by modified Eulerian numbers

Cited by 20 publications

References 13 publications

Power series solution of the fractional logistic equation

Power series solution of the fractional logistic equation

Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system

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

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