How to calculate $E \big[(\int ^{t} _{-\infty} e^{\lambda u} d\tilde{L_\alpha}(u))^A (\int ^{t+h} _{-\infty} e^{\lambda u} d\tilde{L_\alpha}(u))^B\big]$, where \begin{align} \tilde{L}_\alpha (t) = \left\{ \begin{array}{l} L_\alpha(t),\quad t\geq 0 \\ L_\alpha(-t),\quad \text{otherwise} \end{array} \right. \end{align} and a $\{L(t),t\geq0\}$ is $\alpha$-stable Levy motion, thus $L(0)=0$ a.s., has stationary increments and $L(t)-L(s)\sim S_{\alpha}((t-s)^{\frac{1}{\alpha}},\beta,0)$ for any $0\leq s\leq t\leq \infty$ and for some $0<\alpha\leq 2$, $-1\leq\beta\leq1$.
I have to calculate fractional lower order covariance, thus I have \begin{align} FLOC(X(t),X(t+h),A,B)=E \big[\big(\int ^{t} _{-\infty} e^{-\lambda (t-u)} d\tilde{L_\alpha}(u)\big)^A \big(\int ^{t+h} _{-\infty} e^{-\lambda (t+h-u)} d\tilde{L_\alpha}(u)\big)^B\big]=e^{-\lambda t A}e^{-\lambda (t+h) B} E \big[\big(\int ^{t} _{-\infty} e^{\lambda u} d\tilde{L_\alpha}(u)\big)^A \big(\int ^{t+h} _{-\infty} e^{\lambda u} d\tilde{L_\alpha}(u)\big)^B\big], \end{align} with the parameters $A, B\geq 0$ satifying $A+B <\alpha$.