Generalized translation and convolution operators in the realm of linear canonical deformed Hankel transform with applications

Among the class of generalized Fourier transformations, the linear canonical transform is of pivotal importance mainly due to its higher degrees of freedom in lieu of the conventional Fourier and fractional Fourier transforms. This article is a continuation of our recent work "Linear canonical deformed Hankel transform and the associated uncertainty principles, J. Pseudo-Differ. Oper. Appl.(2023), 14:29". Building upon this, we formulate the generalized translation and convolution operators associated with this newly proposed transformation. Besides, the obtained results are invoked to examine and obtain an analytical solution of the generalized heat equation. Finally, we study the heat semigroup pertaining to the generalized heat equation.