A fractional order pine wilt disease model with Caputo–Fabrizio derivative

Abstract

A Caputo-Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are investigated. The existence and uniqueness of the solution for the proposed FPWD model are given via the fixed point theorem. The numerical simulations for the model are obtained by using particular parameter values. The non-integer order derivative provides more flexible and deeper information about the complexity of the dynamics of the proposed FPWD model than the integer order models established before.

Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives

“…Fractional calculus and its applications to real life problems is found extensively in the literature, for example [17][18][19][20][21]. In all these mentioned papers the focus is to eliminate the infection from the community and it is proven that the fractional models have the ability to model such epidemic disease efficiently and provide reasonable results for the case of non-integer.…”

Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

“…To find the answer of this question, the mathematicians have managed to open a new window of opportunities to improve the mathematical modeling of real world problems, which has given birth to many new questions and intriguing results. These newly established results have numerous implementation in many areas of engineering [1,2], such as fractional-order Buck master and diffusion problems [3], fractional-order telegraph model [4,5], fractional KdV-Burger-Kuramoto equation [6], fractal vehicular traffic flow [7], fractional Drinfeld-Sokolov-Wilson equation [8], fractional-order anomalous sub-diffusion model [9], fractional design of hepatitis B virus [10], fractional modeling chickenpox disease [11], fractional blood ethanol concentration model [12], fractional model for tuberculosis [13], fractional vibration equation [14], fractional Black-Scholes option pricing equations [15], fractionally damped beams [16], fractionally damped coupled system [17], fractional-order heat, wave and diffusion equations [18,19], fractional order pine wilt disease model [20], fractional diabetes model [21] etc.…”

Androgen driven evolutionary population dynamics in prostate cancer growth

“…One of the advantage of the fractional calculus is the generalization of the model where one can able to study the dynamics of the model at any arbitrary derivative. The fractional derivative includes the Caputo, Caputo-Fabrizio and the Atangana-Baleanu derivatives which are successfully applied to many problems [17,8,14,15,24,25] and the references therein. In these mentioned papers, the authors used the fractional calculus and applied to the problems in science engineering.…”

“…An analysis of the projective synchronization with in the scope of fractional operators are investigated in [8]. A pine trees dynamics with in the scope of fractional calculus is considered in [14]. The newly very famous derivative known as Atangana-Baleanu derivative is applied to tuberculosis model with relapse in [15].…”

“…Existence and uniqueness for the prostate cancer model. The present section investigates the existence and uniqueness results for the prostate cancer growth model (14). We use the application of fixed point theory to obtain the existence and uniqueness results for the prostate cancer growth model (14).…”