Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed System

Heydari, Mohammad Hossein; Hooshmandasl, Mohammad Reza; Cattani, Carlo; Li, Ming

doi:10.1155/2013/161030

Cited by 33 publications

(12 citation statements)

References 36 publications

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“…The first criticism of the age-structured model is the conversion of the observed size-class data by age class that is required to reconstruct the matrix size of the catch at age data and indices of abundance age used in most models for pelagic species (Shang, 2013b;Heydari et al, 2013;Megrey 1989). Such conversion is particularly uncertain and generates uncertainty in diagnosed stock assessment for yellow mullet.…”

Section: Discussionmentioning

confidence: 99%

Untitled

2015

IJAPR

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The knowledge on size class of yellow mule (Mugil cephalus) is essential to describe a mathematical model on the growth of the species. The objective of this study is to test the growth model of Mugil cephalus population cohort structured in length class frequency. The cohort diet is generally based on plankton at its first stage of growth in the estuary of the River Senegal. A growth software, developed under the FreeFem ++ software has allowed to describe the growth of the population of M. cephalus. The model depicted that the size is the most effective indicator to monitor the growth of yellow mules. The study aims at building a flexible mathematical model that could be used to describe other communities of fish and insects assemblages in order to better understand the growth dynamics of their populations. It is concluded that the use of less variable in the model may make it easier for utilization/application in fisheries management.

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Section: Discussionmentioning

confidence: 99%

Untitled

2015

IJAPR

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“…For that reason, reliable and efficient techniques for the solution of fractional differential equations are indeed required. The most frequently used methods are Walsh functions [5], Laguerre polynomials [6], Fourier series [7], Laplace transform method [8], the Haar wavelets [9], Legendre wavelets [10][11][12], and the Chebyshev wavelets [13,14]. Kronecker operational matrices have been developed by Kilicman and Al Zhour for some applications of fractional calculus [15].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Rational Haar Wavelet and Block Pulse Functions Method for Solving Population Growth Model and Abel Integral Equations

Fathizadeh

Ezzati

Maleknejad

2017

Mathematical Problems in Engineering

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We use a computational method based on rational Haar wavelet for solving nonlinear fractional integro-differential equations. To this end, we apply the operational matrix of fractional integration for rational Haar wavelet. Also, to show the efficiency of the proposed method, we solve particularly population growth model and Abel integral equations and compare the numerical results with the exact solutions.

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“…For in this field memory effects are important, hence it is more realistic to use fractional order derivatives, which express the fact that the next state of the system depends not only upon its current state but also upon all of its historical states (see, e.g., [26][27][28]). Moreover, the above type of nonlinear functions arises also in mathematical problems dealing with heat flow in materials with memory and in viscoelastic problems, where the integral term represents the viscosity part; see, for example, [29].…”

Section: Introductionmentioning

confidence: 99%