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Analysis of an El Nino-Southern Oscillation model with a new fractional derivative. (English) Zbl 1373.86007

Summary: 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.

MSC:

86A10 Meteorology and atmospheric physics
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34K07 Theoretical approximation of solutions to functional-differential equations
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