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

Area of Science:

• Mathematical modeling
• Building energy systems
• Fractional calculus

Background:

• Traditional heating and cooling models lack memory effects.
• Energy efficiency in buildings is a critical research area.
• Fractional calculus offers advanced modeling capabilities.

Purpose of the Study:

• To analyze a fractional version of the building heating and cooling model.
• To incorporate energy efficiency aspects into the fractional model.
• To compare fractional models with classical ones.

Main Methods:

• Application of Caputo fractional derivative, Caputo-Fabrizio, and Atangana-Baleanu derivatives.
• Derivation of analytical solutions using Laplace's transform.
• Simulation analysis to validate physical features.

Main Results:

• Novel analytical solutions were derived for the fractional heating and cooling model.
• Simulation results align with classical observations when fractional order approaches one.
• Fractional models effectively retain memory effects.

Conclusions:

• Fractional derivative models offer superior representation of building thermal dynamics due to memory effects.
• The fractional heating and cooling model enhances energy efficiency analysis.
• This approach provides a more suitable framework for complex thermal systems.