arXiv subjects

Z. S. Mansour

Publications and source records attributed to Z. S. Mansour.

2 recordsLinked to original sources

arXiv2025

On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems

We establish two theorems that illustrate the uniqueness of inverse q-Sturm-Liouville problems based on a specified set of spectral data. The first uniqueness theorem employs the method of transformation operators to provide a q-analog of the Levinson-Marchenko uniqueness theorem. The second uniqueness theorem is a q-analog of the Ashrafyan uniqueness theorem. We introduced a q-analog of the Gelfand-Levitan approach, which involves converting q-difference operators into q-integral operators to prove the theorem.

math.CA↗

arXiv2015

Certain triple q-integral equations involving third Jackson $q$-Bessel functions as kernel

In this paper, we employ the fractional $q$-calculus in solving a triple system of $q$-Integral equations, where the kernel is the third Jackson $q$-Bessel functions. The solution is reduced to two simultaneous Fredholm $q$-integral equation of the second kind. Examples are included. We also apply a result in~[Pacific J. Math. \textbf{275}(1) (2015)63--102] for solutions of dual $q^2$-integral equations to solve certain triple integral equations.

math-ph↗