On solving fractional logistic population models with applications

Ezz-Eldien, S. S.

doi:10.1007/s40314-018-0693-4

Cited by 26 publications

(11 citation statements)

References 54 publications

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“…Other different types of fractional differential equations have been tackled using tau method; see previous studies. [36][37][38] The Van der Pol equation (VDPE) has been considered for the first time by Balthazar Van der Pol (1920) to describe the oscillation in vacuum tube circuits. 39 The classical VDPE can be described by the second-order differential equation:…”

Section: Introductionmentioning

confidence: 99%

Theoretical and spectral numerical study for fractional Van der Pol equation

Ezz-Eldien

2019

Math Methods in App Sciences

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This manuscript concerns with both theoretical and numerical study for a generalized form of fractional Van der Pol equations (FVDPEs). The Schauder fixed point and Banach contraction mapping principles are used for investigating the existence and uniqueness of the considered problem. The second novelty of this manuscript is using the tau method for solving a nonlinear problem (specially FVDPE). The convergence analysis of the suggested approach is also studied.Comparisons with other numerical approaches are introduced for testing the applicability of the current approach.

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Section: Introductionmentioning

confidence: 99%

Theoretical and spectral numerical study for fractional Van der Pol equation

Ezz-Eldien

2019

Math Methods in App Sciences

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“…To the best of our knowledge, the following approximative and numerical schemes are developed for the model problem (1.1)- (1.2). These include the Adams-type predictor-corrector method [1], Bessel-collocation method [27], and the spectral tau method based on shifted Jacobi polynomials [10].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

Izadi

2021

FU Math Inform

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Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms.

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“…How a deadly virus spreads can only be understood and explained through population dynamics. There are several reports on using mathematical models to analyze the population dynamics [1,2,3,4,5,6]. Mathematical modeling of physical situations involves differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical approximations have been applied to gain an insight into the behavior of such models. Research efforts over the years have been on the construction of solutions, reformulations, improvements and applications of (1.5) [5,6,10,11,12]. Recently, the research focus has been on delay differential equations with multi-proportional delays.…”

Section: Introductionmentioning

confidence: 99%

Analyzing population dynamics models via Sumudu transform

Aibinu¹,

Moyo²,

Moyo³

2021

Preprint

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This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. In this paper, population growth models are formulated in the form of delay differential equations of pantograph type which is a general form for the existing models. Innovative ways are presented for obtaining the solutions of population growth models where other analytic methods fail. Stimulating procedures for finding patterns and regularities in seemingly chaotic processes have been elucidated in this paper. How, when and why the changes in population sizes occur can be deduced through this study.

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On solving fractional logistic population models with applications

Cited by 26 publications

References 54 publications

Theoretical and spectral numerical study for fractional Van der Pol equation

Theoretical and spectral numerical study for fractional Van der Pol equation

Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

Analyzing population dynamics models via Sumudu transform

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