We discuss integral estimates for domain of solutions to some canonical Riccati and Sturm–Liouville equations on the line. The approach is applied to Hardy and Poincaré type inequalities with weights.

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard by replacing first- and second-order time derivatives Caputo fractional of corresponding orders, Laplacian operator Sturm–Liouville defined terms right left Riemann–Liouville derivatives. Using method separation variables, derive series representations solut...

this paper deals with the boundary value problem involving the differential equationbegin{equation*}    ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$ begin{equation*}    y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0),end{equation*}where $q(x),  a_1 , a_2$ are  real, $qin l...

in this paper, we obtain a suitable mathematical model for the seismic response of dams. by using the shear beam model (sb model), we give a mathematical formulation that it is a partial differential equation and transform it to the sturm-liouville equation.

In this paper, we obtain a suitable mathematical model for the seismic response of dams. By using the shear beam model (SB model), we give a mathematical formulation that it is a partial differential equation and transform it to the Sturm-Liouville equation.