Functional Laplace Transformations: Theory and Applications
Abstract
This research article introduces a novel extension of the classical Laplace transform within the framework of functional quantum calculus.We define two new classes of integral transforms, namely the ( ) -Laplace transform and the ℎ( ) -Laplace transform, collectively referred to as Functional Laplace Transforms.These transforms may be interpreted as variable-order Laplace-type transformations in which the transformation parameters evolve according to prescribed functional dependencies.Fundamental properties, convolution theorem, and operational rules are established.Illustrative examples demonstrate the applicability of the developed theory to generalized differential and quantum models.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Fractional Differential Equations Solutions
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Global Journal of Pure and Applied Mathematics
- Volume
- 22
- Issue
- 1
- Pages
- 75–83
- Publication date
- 3 January 2026
- Language
- EN