Purpose of the C1 in circuit Diagram is to maintain Vin voltage at certain level.

During Ton ( transistor ON),

Current flows in C1 till its charging, meanwhile L1 will be storing energy.

Once C1 charges, the current flow will be through V1, L1, Ton. Current across Ton is depends on its resistance.

Thank you, but tell me if he average discharging current of the C1 capacitor is equal to the mean value of transistor current (See attached picture), that during State On case ?

The transistor is the component controlled by  α ! (see picture )

Hej,

At steady state, the mean current flowing through a capactor is nul (otherwise, the volatge across it,  and thus the energy stored would diverge). It is a priori not the case for the transistor.

When the transitor is 'on', the drain current is equal to the inductor current. It is ussually assumed that the input current I is constant, i.e. without any ripple. Then, the inductor current when the switch is 'on' is equal to I + some ripple current which comes from the capacitor. During this phase, the drain current is a priori much higher than the current from C1.

Thank you Yoann, so it is not correct ? 

I am afraid it is not.

Thank you Yoann, please tell me if you can help me to design the input capacitor of boost converter ?

Hej,

assume that the current I, drawn from the main power supply, is constant.

Let dI° be the peak-to-peak ripple current in the inductor of inductance L; let dVin be the maximum ripple voltage at the input of your converter (it is yours to choose dVin); let fsw be the switchng frequency of your converte; let dc be the duty cycle.

The charge in the capacitor varies accoding to: q=C1*V=int(i_c*dt).  A charge dQ=dI°/(8*fsw)  is drawn from the input capacitor at each half cycle, you must then choose C1 such that: C1>dI°/(8*fsw*dVin) = Vin*dc/(8*L*fsw²*dVin)

Thank you