  We study the quantum dynamics of relaxation, decoherence and entropy of a
qubit embedded in an anisotropic photonic crystal (PhC) through fractional
calculus. These quantum measurements are investigated by analytically solving
the fractional Langevin equation. The qubit with frequency lying inside the
photonic band gap (PBG) exhibits the preserving behavior of energy, coherence
and information amount through the steady values of excited-state probability,
polarization oscillation and von Neumann entropy. This preservation does not
exist in the Markovian system with qubit frequency lying outside the PBG
region. These accurate results are based on the appropriate mathematical method
of fractional calculus and reasonable inference of physical phenomena.
