A pair of fractional Hankel–Clifford transform on Sobolev-type spaces: theory, examples, and applications

This paper defines two definitions for Sobolev-type spaces using fractional Hankel–Clifford transform pairs. We constructed an example in each space and obtained its solution. We also proved that these spaces are complete. Further, we derived the boundedness properties of the product and convolution of these spaces. Furthermore, we provided some applications of fractional Hankel–Clifford transform pairs to solve analytically generalized homogeneous partial differential equations with variable coefficients. Finally, we illustrated the solution surface profiles for generalized homogeneous partial differential equations with variable coefficients in 3D view to show the analytical solution more elegantly.