Multiplicative Bessel equation and its spectral properties

Abstract

We define a Bessel type equation in multiplicative calculus by some algebraic structures. Eigenfunctions of constructed problem are obtained by power series solution technique. While making these solutions, multiplicative Bessel functions are used strongly. We get a generator for that problem and construct integration representations for multiplicative Bessel functions. Finally, some basic spectral properties of multiplicative Bessel problem are examined in detail.