Fractional models with singular and non-singular kernels for energy efficient buildings

In the current study, we investigate and analyze the fractional version of the heating and cooling model for buildings with energy efficiency. We apply the Caputo fractional derivative, Caputo-Fabrizio, and Atangana-Baleanu in the Caputo sense in the analysis and investigation of the governing model. We derive some novel analytical solutions by means of Laplace's transform. Simulation analysis is carried out in order to shed more light on the physical features of the governing models. To believe the results obtained, the fractional order has been allowed to vary between (0,1], whereupon the physical observations match those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional derivatives.