Fractional Calculus: New Applications in Understanding Nonlinear Phenomena

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

Author(s): Jordan Hristov *

Pp: 85-107 (23)

DOI: 10.2174/9789815051933122030007

* (Excluding Mailing and Handling)

Abstract

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.


Keywords: Caputo-Fabrizio derivative, Duhamel theorem, Heat conduction.

Related Books
© 2024 Bentham Science Publishers | Privacy Policy