A compartmental fractional-order mobbing model and the determination of its parameters

Abstract

In this study, a mathematical model is presented with fractional-order differential equations in the Caputo sense that examines the time-dependent changes of variables representing individuals who are exposed to mobbing, individuals who are not exposed to mobbing, or individuals who gained resistance to mobbing, and individuals who practice mobbing. Existence and uniqueness, and boundedness and non-negativity of the solutions of the proposed model are examined. Additionally, the data set containing the time-dependent changes of these variables has been used as a basis to examine the dynamics in a population. By the data set, the approximate results of 9 different parameters used in the proposed mathematical model with ODE have been found with the lsqcurvefit function. The parameters obtained from the ODE system are rewritten into the proposed fractional model, and the value of the derivative order that gives the minimum error has been investigated. The related Matlab codes are presented in the study. Also, while it is observed that a decrease occurs in the number of individuals exposed to mobbing, there is an increase in the number of individuals who are not exposed to mobbing or who gain resistance to mobbing and individuals who practice mobbing. All the obtained results are shown in graphical detail.

The Sequential Conformable Langevin‐Type Differential Equations and Their Applications to the RLC Electric Circuit Problems

“…In fact, this new definition is an extension of the traditional derivative of a function. We have observed that fractional derivative becomes an important part of scientific world and is mainly used in the field of health such as the growth of COVID-19 [7,8], powerlaw modeling of coronavirus [9], modeling coronavirus disease [10], the Ebola epidemic disease [11], the hantavirus of the European moles [12], and in some mathematical models [13][14][15][16][17]. For more information about conformable derivatives, we advise the readers to look at the works [18][19][20] and the references therein.…”

Approximate‐analytical iterative approach to time‐fractional Bloch equation with Mittag–Leffler type kernel

“…The combination of semi-analytical method and integral transforms is an important tool for solving FDEs. Several integral transforms like Laplace and Sumudu transform combined with different fractional operator like Caputo [13][14][15][16][17][18][19][20], Caputo Fabrizio [21,22], and ABC [23,24] to solve FDE. Literature consists of different methods like fractional homotopy perturbation transform method (FHPTM) [11], q-homotopy analysis method [25], Sumudu residual power series method [26], and operational matrix method [27][28][29] that are used to solve fractional order Bloch equation.…”