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We present timing solutions from the Fermi-LAT observations of gamma-ray pulsars PSR J0835$-$4510 (Vela), PSR J1023$-$5746, PSR J2111$+$4606, and PSR J2229$+$6114. Data ranges for each pulsar extend over a decade. From data analysis we have identified a total of 20 glitches, 11 of which are new discoveries. Among them, 15 glitches are large ones with $Δν/ν\gtrsim10^{-6}$. PSR J1023$-$5746 is the most active pulsar with glitch activity parameter being $A_{\rm g}=14.5\times10^{-7}$\yr~in the considered data span and should be a target for frequently glitching Vela-like pulsars in future observations. We have done fits within the framework of the vortex creep model for 16 glitches with $Δν/ν\gtrsim10^{-7}$. By theoretical analysis of these glitches we are able to obtain important information on the structure of neutron star, including moments of inertia of the superfluid regions participated in glitches and coupling time-scales between various stellar components. The theoretical prediction for the time to the next glitch from the parameters of the previous one is found to be in qualitative agreement with the observed inter-glitch time-scales for the considered sample. Recoupling time-scales of the crustal superfluid are within the range of theoretical expectations and scale inversely with the spin-down rate of a pulsar. We also determined a braking index n=2.63(30) for PSR J2229$+$6114 after glitch induced contributions have been removed.