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This research presents an advanced fractional-order compartmental model designed to delve into the complexities of COVID-19 transmission dynamics, specifically accounting for the influence of environmental pathogens on disease spread. By…

Populations and Evolution · Quantitative Biology 2024-07-09 Moein Khalighi , Faïçal Ndaïrou , Leo Lahti

Meta-heuristic algorithms are widely used to tackle complex optimization problems, including nonlinear, multimodal, and high-dimensional tasks. However, many existing methods suffer from premature convergence, limited exploration, and…

Optimization and Control · Mathematics 2025-10-29 Zhaoqi Sun , Qingsong Wang

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…

Analysis of PDEs · Mathematics 2022-05-03 M. E. Hernández-Hernández , V. N. Kolokoltsov , L. Toniazzi

We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (0,1)$ in the time variable $t$ and the first order derivatives in spatial variables…

Analysis of PDEs · Mathematics 2013-09-10 Anatoly N. Kochubei

In this paper, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for…

Numerical Analysis · Mathematics 2019-12-20 Fabio Camilli , Serikbolsyn Duisembay

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference…

Analysis of PDEs · Mathematics 2018-02-01 Zhengguang Liu , Aijie Cheng , Xiaoli Li , Hong Wang

In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order time-fractional partial differential equations; nonlinear and linear in respect to spatial and temporal…

Analysis of PDEs · Mathematics 2020-03-31 Moein Khalighi , Mohammad Amirian Matlob , Alaeddin Malek

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…

Numerical Analysis · Mathematics 2025-01-17 M. -C. Casabán , R. Company , V. N. Egorova , L. Jódar

A Caputo fractional-order mathematical model for the transmission dynamics of tuberculosis (TB) was recently proposed in [Math. Model. Nat. Phenom. 13 (2018), no. 1, Art. 9]. Here, a sensitivity analysis of that model is done, showing the…

Optimization and Control · Mathematics 2019-08-12 Silverio Rosa , Delfim F. M. Torres

In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…

General Mathematics · Mathematics 2026-04-16 Vivek Mishra , S. Das

In this paper, the authors study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a…

Optimization and Control · Mathematics 2019-07-25 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-11-28 Max Carlson , Robert M. Kirby , Hari Sundar

A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…

Numerical Analysis · Mathematics 2021-11-01 Daegeun Yoon , Donghyun You

In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…

Atmospheric and Oceanic Physics · Physics 2018-12-26 A. G. Goulart , M. J. Lazo , J. M. S. Suarez

In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…

Numerical Analysis · Mathematics 2023-05-23 Peyman Alipour

In this work, we investigate a fractional-order tumor growth model aimed at capturing memory effects and nonlocal temporal dynamics inherent to tumor evolution. The model is formulated using Caputo fractional derivatives and incorporates…

Medical Physics · Physics 2026-03-17 Karen Escutia , Carlos Islas , Pablo Padilla

In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…

Mathematical Physics · Physics 2014-10-30 P. Artale Harris , R. Garra

The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…

Numerical Analysis · Mathematics 2018-02-14 Riccardo Fazio , Alessandra Jannelli

A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…

Analysis of PDEs · Mathematics 2017-04-20 Yoshikazu Giga , Tokinaga Namba

In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rectangular domains solutions is obtained in the form of the…

Analysis of PDEs · Mathematics 2016-10-18 M. O. Mamchuev