A Discretization Approach for the Nonlinear Fractional Logistic Equation

Izadi, Mohammad; Srivástava, H. M.

doi:10.3390/e22111328

Cited by 31 publications

(9 citation statements)

References 39 publications

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“…This trend found applications in numerous disciplines; a famous example is in the growth of tumors in medicine [ 18 ]. In [ 19 ], the authors replaced the differential operator d/d t in Eq. ( 4 ) by ( ) denoting the fractional differential operator of Caputo type, then used Galerkin method for its solution.…”

Section: Methodsmentioning

confidence: 99%

Modeling the COVID-19 spread, a case study of Egypt

Deif

El‐Naggar

2021

J Egypt Math Soc

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In this article, the authors applied a logistic growth model explaining the dynamics of the spread of COVID-19 in Egypt. The model which is simple follows well-known premises in population dynamics. Our aim is to calculate an approximate estimate of the total number of infected persons during the course of the disease. The model predicted—to a high degree of correctness—the timing of the pandemic peak$$t_{{\text{m}}}$$ t m and the final epidemic size$$P$$ P ; the latter was foreseen by the model long before it was announced by the Egyptian authorities. The estimated values from the model were also found to match significantly with the nation reported data during the course of the disease. The period in which we applied the model was from the first of April 2020 until the beginning of October of the same year. By the time the manuscript was returned for revision, the second wave swept through Egypt and the authors felt obliged to renew their study. Finally, a comparison is made with the SIR model showing that ours is much simpler; yet leading to the same results.

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Section: Methodsmentioning

confidence: 99%

Modeling the COVID-19 spread, a case study of Egypt

Deif

El‐Naggar

2021

J Egypt Math Soc

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“…Most models explored and analyzed under the FC framework use the Caputo operator. Momani and Shawagfeh provide several basic works of fractional calculus on various aspects [1]: Podlubny [2], Jafari and Seifi [3,4], Kiryakova [5], Oldham and Spanier [6], Miller and Ross [7], Diethelm et al [8], Trujillo [9], Kilbas and Kemple and Beyer [10] and so on [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

et al. 2023

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In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differentiation. This equation has been used in the study of quantum dynamics to model the behavior of particles with fractional spin. The Laplace transform is employed to transform the equations into a simpler form, and the resulting equations are then solved using the proposed methods. The accuracy and efficiency of the method are demonstrated through numerical simulations, which show that the method is superior to existing numerical methods in terms of accuracy and computational time. The proposed method is applicable to a wide range of fractional-order differential equations, and it is expected to find applications in various areas of science and engineering.

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“…The main capability of of the proposed Bessel spectral algorithm is that it converts the SFDEs (1) to a system of algebraic equations while reducing computational complexity. Usages of the proposed technique but with different bases such as Legendre, Chebyshev, Chelyshkov, alternative Bessel, and Jacobi functions can be found in [31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations

Izadi

Srivástava

Adel

2022

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In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system of algebraic equations and by solving this system the unknown Bessel coefficients are determined and the solution will be known. The method is tested on several test examples and proves to provide accurate results as compared to other existing methods from the literature. The simplicity and robustness of the proposed technique drive us to investigate more of their applications to several similar problems in the future.

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A Discretization Approach for the Nonlinear Fractional Logistic Equation

Cited by 31 publications

References 39 publications

Modeling the COVID-19 spread, a case study of Egypt

Modeling the COVID-19 spread, a case study of Egypt

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations

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