Analysis of an El Nino-Southern Oscillation model with a new fractional derivative

Abstract In this article, we analyze the El Nino–Southern Oscillation (ENSO) model in the global climate with a new fractional derivative recently proposed by Caputo and Fabrizio. We obtain the solution by using the iterative method. By using the fixed-point theorem the existence of the solution is discussed. A deeply analysis of the uniqueness of the solution is also discussed. And to observe the effect of the fractional order we presented some numerical simulations.