Boost converter capacitor charging question
When the inductor is charging, the capacitor current should be decreasing because its supplying the load.


Usually we design so that the droop of the capacitor voltage  as it discharges is small relative to the average output voltage (another way to say this is, the ripple voltage is small), and so we neglect the change of capacitor current during discharge when hand-calculating.


  When the inductor is discharging (after DT), the capacitor should be charging and hence the current should be increasing, but in the figure its decreasing, why is that so ?


Note the figure uses passive sign convention. Positive capacitor current is charging the capacitor and negative capacitor current is discharging it. As long as the capacitor current is positive, the capacitor is charging, no matter whether the magnitude of the current is increasing or decreasing.

In this part of the cycle, the capacitor is absorbing the part of the inductor current that is not flowing to the load (which is taking a nearly constant current because, again, we're assuming a small ripple voltage). So if the inductor current is decreasing, the capacitor current has to be decreasing also.