The Duhamel Method in Transient Heat Conduction: A Rendezvous of Classics and Modern Fractional Calculus

This chapter presents an attempt to demonstrate that the Duhamel theorem applicable for time-dependent boundary conditions (or time-dependent source terms) of heat conduction in a finite domain and the use of the Fourier method of separation of variable (superposition version) naturally lead to appearance of the Caputo- Fabrizio operators in the solution. The fractional orders of the emerging series of Caputo-Fabrizio operators are directly related to the eigenvalues determined by the Fourier’s method. The general expression of the solution in terms of Caputo-Fabrizio operators has been developed followed by four examples.