In the current paper , we further develop the model for the migration of planets introduced in Del Popolo et al .
( 2001 ) and extended to time-dependent planetesimal accretion discs in Del Popolo & Ekşi ( 2002 ) .
We use a method developed by Stepinski & Valageas ( 1996 , 1997 ) , that is able to simultaneously follow the evolution of gas and solid particles for up to 10 ^ { 7 } { yr } .
The disc model is coupled to the migration model introduced in Del Popolo et al .
( 2001 ) in order to obtain the migration rate of the planet in the planetesimal disc .
We find that in the case of discs having total mass of 10 ^ { -3 } -0.1 M _ { \odot } , and 0.1 < \alpha < 0.0001 , planets can migrate inward a large distance while if M < 10 ^ { -3 } M _ { \odot } the planets remain almost in their initial position for 0.1 < \alpha < 0.01 and only in the case \alpha < 0.001 
the planets move to a minimum value of orbital radius of \simeq 2 { AU } .
The model gives a good description of the observed distribution of planets in the period range 0-20 days .