A method for study of critical behaviour in non-integer space dimension is discussed. Critical exponents of the Ising-like and O(m)-symmetrical systems are calculated in the case, when the dimension of space is non-integer. Calculations are performed in the frames of the fixed-dimension field theoretical approach. Renormalization group functions in the Callan-Symanzik scheme are considered directly in non-integer dimensions. Perturbation theory expansions are resummed with the use of Pade-Borel transformation.