On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d$ Yokoi's $d$-invariants by reference to continued fraction  expansion of integral basis element where $ell left({d}right)$ is a period length.  Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.