Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition

Abstract

The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically.

Nonlocal <span aria-describedby="tippy-18">Boundary Problem for a Loaded Equation of Mixed Type in a Special Domain

“…Melisheva [12][13]. Boundary value problems for an equation of hyperbolic type with a fractional derivative were also studied in works [30][31][32][33].…”

“…Theorem 2. If conditions (2), ( 10), (30), (32) are met, then Ω j+2 the solution to the problem Γ j exists and is unique in the domain.…”