Abstract
(is article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by D-ABC(alpha)[v(i)](t)] is an element of Y-i{vi(t)(i-1)(infinity). The mappings y(i)(t,] {v(i) (t)(i-1)(infinity)) are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition sigma v(i) (0)= gamma v(i) (rho), sigma, c is an element of R. (is type of condition is the generalization of periodic, almost, and antiperiodic types.