The mathematical study of climate change model under nonlocal fractional derivative

Abstract Adjusting of species with the rapid change that occurs in the conditions of various ecosystems and environment behavior are not easy for them with the passage of time. One can expect species fight against these forces to get rid of extinction, i.e., species tend to adapt genetically or move to a new environment to resilience against extinction. In this paper, a climate change model is investigated by Caputo fractional derivative. Firstly, the qualitative analysis of the solution of the fractional Climate Change model is found by the application of the theory of fixed point. For approximate solution, the iterative numerical techniques of the consider problem under Caputo derivative is presented. In the last part, the numerical approximation of plotting are provided for validation of our fractional-order iterative scheme. As a whole, the total spectrum lying between two integer values are achieved with more information about the complexity of the dynamics of the proposed fractional Climate Change-model.