The paper deals with asymptotics of eigenvalues and equiconvergence theorems connected with the operator d/dt considered with integral ”boundary value condition” \(\int^{a}_{-a}y(t)k(t)/(a-| t|)^{\alpha}dt=0,\) \(0<\alpha <1\), \(k\in BV[-a,a]\), \(k(a- 0),k(a+0)\neq 0\) and for the operator \(d^ n/dt^ n\) considered with ”boundary value conditions” including fractional derivatives: \(U_{\nu}(y)=\alpha_{\nu}(-1)^{p_{\nu}}D^{k_{\nu}}y(- a)+\beta_{\nu}D^{k_{\nu}}y(a)=0,\) \(\nu =1,...,n\), \(n-1\geq k_ 1\geq...\geq k_ n>-1\), \(k_{\nu +2}<k_{\nu}\), \(-1\leq p_{\nu}- 1<k_{\nu}\leq p_{\nu}\leq n-1\) where \(p_{\nu}\) are integers.