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Abstract In this work, we study the diabetes model and its complications with the Caputo–Fabrizio fractional derivative. A deterministic mathematical model pertaining to the fractional derivative of the diabetes mellitus is discussed. The analytical solution of the diabetes model is derived by exerting the homotopy analysis method, the Laplace transform and the Padé approximation. Moreover, existence and uniqueness of the solution are examined by making use of fixed point theory and the Picard–Lindelof approach. Ultimately, for illustrating the obtained results some numerical simulations are performed.