Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel subfusion sequences and subfusion frames and we investigate the relationship between their operation. Also, the definition of the orthogonal complement of subfusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these no...

We introduce integral transforms to study problems for the singular Bessel differential operators B−γ with negative parameter −γ < 0. A solution equation B−γu+u = 0 is a function u

We study a modified version of an equation of the continuous Toda type in 1+1 dimensions. This equation contains a friction-like term which can be switched off by annihilating a free parameter ǫ. We apply the prolongation method, the symmetry and the approximate symmetry approach. This strategy allows us to get insight into both the equations for ǫ = 0 and ǫ 6= 0, whose properties arising in th...

n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

Acoustic waves in a rigid axisymmetric tube with a variable cross-section are considered. The governing Helmholtz equation is solved using Neumann series (expansions in Bessel functions of various orders) with a stretched radial coordinate, leading to a hierarchy of one-dimensional ordinary differential equations in the longitudinal direction. The lowest approximation for axisymmetric motion in...

New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth order partial differential equation.