Analysis for fractional‐order predator–prey model with uncertainty

Abstract

Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.

A Review on Fuzzy Differential Equations

“…Indeed, the applications of FDEs are not limited to the theory of control, but they have been proposed in studying biomathematics [192], diabetes mellitus [193], [194], cerebrospinal fluid pressure [126], hydrologic process [195], water movement in a horizontal column [196], epidemic model [197], population growth model [82], [98], Newton's law of cooling [72], electric circuits [72], [198], and the brain tumor [199]. Moreover, some of the other proposed applications of FDEs can be found in [200] for a predatorprey model, in [201] for production inventory model, in [72] for an economical investment, and in [202] for oil palm frond. For further applications of FDEs refer to [203]- [205].…”

Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order

“…Different types of fuzzy (and interval) time-fractional dynamical models for different biological systems have been discussed in (Chakraverty et al. , 2020; Narayanamoorthy et al. , 2019; Rahman et al.…”

“…Several works have been conducted in the field of fuzzy fractional derivatives, and differential equations (Van Hoa, 2015;Chakraverty et al, 2016;Mazandarani and Najariyan, 2014b). Different types of fuzzy (and interval) time-fractional dynamical models for different biological systems have been discussed in (Chakraverty et al, 2020;Narayanamoorthy et al, 2019;Rahman et al, 2020) using various computationally efficient methods.…”

The Ratio Predator-Prey Model with Random Initial Conditions

“…The influence of fuzziness has been studied in [2][3][4], and the authors used different approaches to deal with uncertainty in the predator-prey model. Narayanamoorthy et al analyzed the fractional-order predator-prey model by taking the initial conditions of the predator-prey model as fuzzy initial conditions [5]. Another powerful approach for dealing with uncertainty in models is probability theory, which is used when constructing a random mathematical model.…”