Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

Boundary Element Analysis of Nonlinear Heat Conduction Problem with Point, Line and Distributed Heat Sources Employing Analytical integrations

Boundary Element Analysis of Nonlinear Heat Conduction Problem with Point, Line and Distributed Heat Sources Employing Analytical integrations

Fourier's law of heat conduction: quantum mechanical master equation analysis.

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effec...

Reconstruction of the Boundary Condition for the Heat Conduction Equation of Fractional Order

This paper describes reconstruction of the heat transfer coefficient occurring in the boundary condition of the third kind for the time fractional heat conduction equation. Fractional derivative with respect to time, occurring in considered equation, is defined as the Caputo derivative. Additional information for the considered inverse problem is given by the temperature measurements at selecte...

Numerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...