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Simple 1-D semi-infinite heat conduction problems enable to demonstrate the  potential of the fractional calculus in determination of transient thermal  impedances under various boundary conditions imposed at the interface (x=0).  The approach is purely analytic and very effective because it uses only  simple semi-derivatives (half-time) and semi-integrals and avoids  development of entire domain solutions. 0x

Thermal impedance estimations by semi-derivatives and semi-integrals: 1-D semi-infinite cases