In this paper, we investigate the resolvent operator of singular q-Sturm-Liouville problem defined as − ( 1 / q ) D ⁻ ¹ [D y x )] + [r - λ ]y )=0 −(1/q)Dq⁻¹Dqy(x)+r(x)y(x)=λy(x) , with boundary condition 0 c o s β i n = y(0,λ)cosβ+Dq⁻¹y(0,λ)sinβ=0 where ∈ C λ∈C $r$ is a real function on $[0,∞)$, continuous at zero and r L l ∞ r∈Lq,loc¹(0,∞) . We give an integral representation for some properti...

<abstract><p>In this paper, we present a general formulation of the well-known fractional drifts Riemann-Liouville type. We state main properties these integral operators. Besides, study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving operators.</p></abstract>

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several generalizations of formula for generalized functions polynomials. As a consequence, give new addition an integral representation these Finally, introduce family Lebesgue spaces show that some special belong to them.