*Correspondence: [email protected] 1School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China Full list of author information is available at the end of the article Abstract This paper is concerned with the solvability for fractional Sturm-Liouville boundary value problems with p(t)-Laplacian operator at resonance using Mawhin’s continuation theorem. Suffic...

Riesz potentials also called Riesz fractional derivatives and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions ζ s, a and ζ− s, a . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are establishe...

We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α ∈ (3/2, 2) on the unit interval (0, 1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα−1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value pro...

Abstract In this paper, we are concerned with the eigenvalue gap and ratio of Dirichlet conformable fractional Sturm–Liouville problems. We show that kind differential equation satisfies property by Prüfer substitution. That is, n th eigenfunction has $n-1$ n − 1 zero in $( 0...

In the present paper, we are concerned with a fractional wave equation of Sturm–Liouville type in general star graph. We first give several existence, uniqueness and regularity results weak solutions for one-dimensional case using spectral theory; prove existence to quadratic boundary optimal control problem provide characterization via Euler–Lagrange first-order optimality conditions. then inv...