A FRACTIONAL PREDATOR-PREY MODEL WITH ALLEE EFFECT AND CONSTRUCTIVE IMPACT ON PREY CARRYING CAPACITY

This paper explores a prey-predator model that incorporates several biological phenomena, with a focus on the positive feedback that certain prey species have on their own carrying capacity. Traditional models treat carrying capacity as a constant; however, this study assumes a variable carrying capacity influenced by the prey population. To account for the memory effect and hereditary properties within biological systems, we employ fractional differential equations using the Caputo fractional derivative. Additionally, we incorporate the Allee effect, which plays a critical role in population dynamics, especially at low population densities. Through numerical analysis, the model's stability and dynamic behavior are examined, providing insights into species coexistence, population cycles, and extinction risks. This framework aims to enrich existing models and offer a more comprehensive understanding of prey-predator interactions with prey species impacting their carrying capacity.