  Observations of diffuse Galactic gamma-ray spectrum by the EGRET instrument
reveal an excess above ~ 1 GeV over the expected gamma-ray spectrum calculated
under the assumption that the locally observed cosmic-ray (CR) spectra
represent the galactic CR spectra. Assuming that Galactic CRs of energy below ~
100 TeV are accelerated by supernova remnant (SNR) shock waves and that the
shock compression ratio is SNR age dependent, the average source injection
spectra from an ensemble of SNRs is calculated both in the inner (330<l<30) and
outer (30<l<330) regions of the galaxy. The calculation considers the SNR age
distribution in the galaxy. Injecting these spectra in the galaxy and using a
3-D convection-diffusion equation, the CR electrons and protons spectra in the
two galactic regions are obtained and their spectra in the galactic disk are
found to be flatter than the observed CR spectra. The diffuse gamma-ray
spectrum produced by the interaction of these galactic CRs with the ISM and
ISRFs is compared with the experimental data in both the galactic regions.
Furthermore, the steepening of the observed local CR spectra from the galactic
disk CR spectra are discussed by propagating local CRs having a source spectrum
derived using local SNR age distribution (SNRs located within 1.5 kpc from the
Sun), for a diffusion coefficient D_0 ~ 0.3\times 10^{27} cm^2 s^{-1} in the
local region which is much less than the typical value in the galaxy D_0 ~
(1-10)\times 10^{28} cm^2 s^{-1}. The results obtained in this paper support
the SNR origin of galactic CRs.
