  VLA observations at 1477 MHz revealed the presence of a radio mini-halo
surrounding the faint central point-like radio source in the Ophiuchus cluster
of galaxies. In this work we present a study of the radio emission from this
cluster of galaxies at lower radio frequencies. We observed the Ophiuchus
cluster at 153, 240, and 614 MHz with the GMRT. The mini-halo is clearly
detected at 153 and 240 MHz while it is not detected at 610 MHz. The most
prominent feature at low frequencies is a patch of diffuse steep spectrum
emission located at about 5' south-east from the cluster center. By combining
these images with that at 1477 MHz, we derived the spectral index of the
mini-halo. Globally, the mini-halo has a low-frequency spectral index of
alpha_240^153 ~1.4 +/- 0.3 and an high-frequency spectral index of
alpha_1477^240 ~ 1.60 +/- 0.05. Moreover, we measure a systematic increase of
the high-frequency spectral index with radius: the azimuthal radial average of
alpha_1477^240 increases from about 1.3, at the cluster center, up to about 2.0
in the mini-halo outskirts. The observed radio spectral index is in agreement
with that obtained by modeling the non-thermal hard X-ray emission in this
cluster of galaxies. We assume that the X-ray component arises from inverse
Compton scattering between the photons of the cosmic microwave background and a
population of non-thermal electrons which are isotropically distributed and
whose energy spectrum is a power law with index p. We derive that the electrons
energy spectrum should extend from a minimum Lorentz factor of gamma_min < 700
up to a maximum Lorentz factor of gamma_max =3.8 x 10^4 with an index p=3.8 +/-
0.4. The volume-averaged strength for a completely disordered intra-cluster
magnetic field is B_V ~0.3 +/- 0.1 micro-G.
