G-quadruplex DNA (GqDNA) structures act as promising anticancer targets for small-molecules (ligands). Solvation dynamics of a ligand (DAPI: 4′,6-diamidino-2-phenylindole) inside antiparallel-GqDNA is studied through direct comparison of time-resolved experiments to molecular dynamics (MD) simulation. Dynamic Stokes shift of DAPI in GqDNA prepared in H2O-buffer and D2O are compared to find the effect of water on ligand solvation. Experimental dynamics (in H2O) is then directly compared to the dynamics computed from 65 ns simulation on same DAPI-GqDNA complex. Ligand solvation follows power-law relaxation (summed with fast exponential relaxation) from ~100 fs to 10 ns. Simulation results show relaxation below ~5 ps is dominated by water motion, while both water and DNA contribute comparably to dictate long-time power-law dynamics. Ion contribution is however found to be negligible. Simulation results also suggest that anomalous solvation dynamics may have origin in subdiffusive motion of perturbed-water near GqDNA.