Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiabi...

Full description

Saved in:

Bibliographic Details
Published in:	Advances in difference equations Vol. 2019; no. 1; pp. 1 - 34
Main Authors:	Khan, Najeeb Alam, Razzaq, Oyoon Abdul, Mondal, Sankar Parsad, Rubbab, Qammar
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 23-09-2019 Springer Nature B.V SpringerOpen
Subjects:	Advances in Fractional Differential Equations and Their Real World Applications - Part Two Analysis Biological models (mathematics) Difference and Functional Equations Fractional generalized Hukuhara differentiable Functional Analysis Fuzzy fractional Laplace transform Laplace transforms Mathematics Mathematics and Statistics Order parameters Ordinary Differential Equations Partial Differential Equations Population growth Routh–Hurwitz condition Runge-Kutta method Stability analysis Triangular fuzzy number Fractional generalized Hukuhara differentiable Routh–Hurwitz condition Stability analysis Fuzzy fractional Laplace transform Triangular fuzzy number
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh–Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge–Kutta method (FFRK), Grunwald–Letnikov’s definition (GL) and Adams–Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations.
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-019-2331-x