241 documents found, page 1 of 25
The non-population conserving SIR model on time scales
Belarbi, Zahra; Bayour, Benaoumeur; Torres, Delfim F. M.We investigate the non-conserving Susceptible–Infected–Removed epidemic population model on time scales (shortly denoted by SIR-NC) to describe the spread of infections in a community. After a brief introduction to the theory of time scales, we formulate mathematically our dynamic SIR-NC system on time scales and derive its analytical solution. The obtained results unify and extend those of the continuous and d...
Controllability and observability of tempered fractional differential systems
Lamrani, Ilyasse; Zitane, Hanaa; Torres, Delfim F. M.We study controllability and observability concepts of tempered fractional linear systems in the Caputo sense. First, we formulate a solution for the class of tempered systems under investigation by means of the Laplace transform method. Then, we derive necessary and sufficient conditions for the controllability, as well as for the observability, in terms of the Gramian controllability matrix and the Gramian ob...
Fractional modelling of COVID-19 transmission incorporating asymptomatic and su...
Khalighi, Moein; Lahti, Leo; Ndaïrou, Faïçal; Rashkov, Peter; Torres, Delfim F. M.The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differentia...
A model for the dynamics of COVID-19 infection transmission in human with laten...
Chatterjee, Amar N.; Abraha, Teklebirhan; Al Basir, Fahad; Torres, Delfim F. M.In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a ’latent period’ and ’the time for immune response’ as delay parameters, allowing us to study the effects of time delays in human COVID-19 infection. We have determined the equilibrium points and analyzed their stability. The disease-free equilibrium...
Fractional differential equations of a reaction-diffusion SIR model involving t...
Zinihi, Achraf; Ammi, Moulay Rchid Sidi; Torres, Delfim F. M.The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and employing the $p$-Laplacian operator. The immunity is imposed through the vaccination program, which is regarded as a control variable. Finding the optimal control pair that reduces the number of sick people, the associated vaccination...
Stability criteria of nonlinear generalized proportional fractional delayed sys...
Zitane, Hanaa; Torres, Delfim F. M.This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Gr\"onwall inequality, we derive an explicit criterion that enables the system trajectories to stay within a priori given sets during a pre-specified time interval, in terms of the Mittag-Leffler function. Then, we investigate the finite time stability of no...
Mathematical Analysis: Theory and Applications
Debnath, Pradip; Srivastava, H. M.; Torres, Delfim F. M.; Cho, Yeol JeMathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics. Readers will discover numerous valuable tools and techniques to enhance their understanding of recent advancements in mathematical analysis and its applications. Each chapter highlights new research directions,...
Fractional calculi on time scales: differentiation and integration of a functio...
Torres, Delfim F. M.We review the concept of fractional differentiation and fractional integration on time scales of a function with respect to another function. Applications and future possible developments are given.
The duality theory of fractional calculus and a new fractional calculus of vari...
Torres, Delfim F. M.Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractio...
Modeling blood alcohol concentration using fractional differential equations ba...
Wanassi, Om Kalthoum; Torres, Delfim F. M.We propose a novel dynamical model for blood alcohol concentration that incorporates -Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol concentration in the stomach and the alcohol concentration in the blood of an individual. These analytical formulas provide us a straightforward numerical scheme, which demonstrates...