<p>Global climate change is intensifying, with rising temperatures significantly impacting ecological relationships. Understanding the connection between temperature and predation is imperative to address the threat of extinction resulting from excessive temperature increases. In this paper, we introduce a fractional prey-predator model incorporating the Caputo fractional operator. Our model considers prey-predator interactions based on Crowley and Martin’s functional response, accounting for the fear effect induced by predation. We analyze the non-negativity, existence, uniqueness, and boundedness of solutions within our model, considering both classical and Caputo derivative scenarios. Additionally, we investigate the local stability of each equilibrium under both integer and fractional-order conditions, emphasizing the global stability of the coexistence positive equilibrium point in both contexts. Our examination treats predation as a time-dependent function, with the temperature function reflecting climate change and elucidating how rising temperatures contribute to predation. Through numerical simulations, we explore the impacts of fear on prey behavior and population dynamics, and illustrate how climate change, especially rising temperatures, intricately affects species relationships.</p>