A Mathematical Insight of Fractional Logistic Equation of Variable Order on Finite Intervals

Abstract

The logistic equation, which is usually represented as a differential equation, is used to simulate the population expansion or the spread or evolution of phenomena within a confined area. However, it is frequently discussed in terms of the evolution of solutions in unbounded time and the longterm behavior of the population size. In this paper, we analyze it by using variable order fractional calculus within the constraint of a finite time frame, allowing for a more realistic and applicable assessment of real-world scenarios with finite resources or boundaries.