A novel matrix approach to fractional finite difference for solving models based on nonlinear fractional delay differential equations

Abstract

Many real-life phenomena in physics, engineering, biology, medicine, economics, etc. can be modeled by fractional delay differential equations and having in mind that these modeling interpret phenomena better, they are noticed by researchers, engineers, and mathematicians. In this paper the method of fractional finite differences has been presented and used for numerical solution of such models and used for solving a number of famous fractional order version of models such as the fractional order version of Hutchinson model is related to rate of population growth, the fractional order version of Verhulst Pearl model is related to the impact of a specific factor on the changes of population in an area model, fractional order version of the negative impact of population growth in a specific time and model of fractional order version of the four years life cycle of a population of lemmings. The proposed method besides being simple is so exact which is sensible in the solved problems