Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

In this study we consider the Kaup–Boussinesq system with a self-consistent source. We show that source can be integrated by method of inverse scattering theory. For solving problem under consideration, use direct and Sturm–Liouville equation an energy-dependent potential. The time evolution data for potentials associated solution is determined. obtained equalities completely determine any $t$,...

Consider the Sturm-Liouville problem on a finite interval with Dirichlet boundary conditions. Let the elastic modulus and the density be of bounded variation. Results for both the forward problem and the inverse problem are established. For the forward problem, new bounds are established for the eigenfrequencies. The bounds are sharp. For the inverse problem, it is shown that the elastic modulu...