Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium

Yu, Bo; Jiang, Xiaoyun; Wang, Chu

doi:10.1016/j.amc.2015.10.081

Cited by 37 publications

(9 citation statements)

References 39 publications

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“…[142] , [143] , [144] , [145] , [146] , [147] , [148] , [149] , [150] , [151] , [152] , [153] , [154] , [155] , [156] , [157] , [158] , [159] , [160] , [161] , [162] , [163] , [164] , [165] , [166] , [167] , [168] , [169] , [170] , [171] , [172] , [173] , [174] , [175] , [176] …”

Section: Uncited Referencesunclassified

Review of fractional epidemic models

Chen

Liu

et al. 2021

Applied Mathematical Modelling

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The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR),Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

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Section: Uncited Referencesunclassified

Review of fractional epidemic models

Chen

Liu

et al. 2021

Applied Mathematical Modelling

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“…Often, for many practical studies, there is an unknown parameter that is found in the initial or boundary data or the source term that requires an additional measurement. The inverse fractional-order case introduces an appropriate instrument for describing anomalous diffusion phenomena appeared in chemical [16], biological [17,18], hydrological [19], physical [20,21] and engineering [22,23] fields. In contrast to those classical problems, the studies of inverse problems have not satisfactorily been studied.…”

Section: Introductionmentioning

confidence: 99%

Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations

et al. 2021

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In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The proposed scheme is based on a spectral collocation approach to obtain the two independent variables. Our approach is accurate, efficient, and feasible for the model problem under consideration. The proposed Jacobi spectral collocation method yields an exponential rate of convergence with a relatively small number of degrees of freedom. Finally, a series of numerical examples are provided to demonstrate the efficiency and flexibility of the numerical scheme.

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“…coefficient information, source term information might not be given and then we need to recover them by extra measured information which is able to yield some fractional diffusion inverse problems [12][13][14][15][16][17][18][19][20]. In recent years, inverse problems for fractional diffusion equation have become very active in various fields of sciences and engineering, such as biology [21,22], physics [23,24], chemistry [25], and hydrology [26].…”

Section: Introductionmentioning

confidence: 99%

An Inverse Source Problem of Space-Fractional Diffusion Equation

Liu

Feng

Zhang

2021

Bull. Malays. Math. Sci. Soc.

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This paper is devoted to an inverse space-dependent source problem for spacefractional diffusion equation. Furthermore, we show that this problem is ill-posed in the sense of Hadamard, i.e., the solution (if it exists) does not depend continuously on the data. In addition, we propose a simplified generalized Tikhonov regularization method and prove the corresponding convergence estimates by using a priori regularization parameter choice rule and a posteriori parameter choice rule, respectively. Finally, numerical examples are carried to support the theoretical results and illustrate the effectiveness of the proposed method.

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Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium

Cited by 37 publications

References 39 publications

Review of fractional epidemic models

Review of fractional epidemic models

Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations

An Inverse Source Problem of Space-Fractional Diffusion Equation

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