The continuous fractional Bessel wavelet transform and its applications

Characterizations of Continuous Fractional Bessel Wavelet Transforms

“…Discussions such as those presented in this sequel were initiated by Srivastava et al [8]. Some interesting applications of the fractional-order Bessel wavelet transform in the areas of time-invariant linear filters and integral equations involving the fractional wavelet in the kernel can be found in several recent works (see, for example, [12]; see also [28][29][30]).…”

“…In this section, our main object is to study the continuous fractional Bessel wavelet transform and to develop its various properties by applying the theory of the fractional Hankel transformation. Definition 3 (see [12]). Let the function ψ ∈ L p σ (I) be given for…”

“…Definition 4 (see [12]). By taking the function ψ ∈ L 2 σ (I) and the fractional wavelet ψ b,a 1 α (x) given by Definition 3, the fractional Bessel wavelet transform B ψ f (b, a) is defined for 0 < α 1 by…”

“…Definition 1 (see [3,12]). For each φ ∈ L 1 σ (I), the fractional Hankel transform of the function φ is defined by…”

“…In order to define the continuous fractional Bessel wavelet transform, we shall need the definition of the fractional Hankel convolution, which is given below. Definition 2 (see [12]). Let φ ∈ L 1 σ (I) and ψ ∈ L 1 σ (I).…”