The radio evolution of , so far the youngest known , Galactic supernova remnant ( SNR ) G1.9+0.3 is investigated by using three-dimensional ( 3D ) hydrodynamic modelling and non-linear kinetic theory of cosmic ray ( CR ) acceleration in SNRs . We include consistent numerical treatment of magnetic field amplification ( MFA ) due to resonant streaming instability . Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova explosion located near the Galactic Centre , using widely accepted values for explosion energy 10 ^ { 51 } erg and ejecta mass 1.4 M _ { \sun } , the non-thermal continuum radio emission is calculated . The main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution . We estimate that the SNR is now \sim 120 yr old , expanding in an ambient density of 0.02 cm ^ { -3 } , and explain its steep radio spectral index only by means of efficient non-linear diffusive shock acceleration ( NLDSA ) . We also make comparison between simulations and observations of this young SNR , in order to test the models and assumptions suggested . Our model prediction of a radio flux density increase of \sim 1.8 per cent yr ^ { -1 } during the past two decades agrees well with the measured values . We synthesize the synchrotron spectrum from radio to X-ray and it fits well the Very Large Array , Molonglo Observatory Synthesis Telescope , Effelsberg , Chandra and NuSTAR measurements . We also propose a simplified evolutionary model of the SNR in gamma rays and suggest it may be a promising target for gamma-ray observations at TeV energies with the future generation of instruments like Cherenkov Telescope Array . SNR G1.9+0.3 is the only known Galactic SNR with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now . We conclude that this is a general property of SNRs in free expansion phase .