A new integral transform and its applications. (English) Zbl 1349.44001
Summary: The authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, include (for example) existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the \(H\)-function and the \(\mathbf{H}\)-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.
MSC:
44A10 | Laplace transform |
44A20 | Integral transforms of special functions |
33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
35A22 | Transform methods (e.g., integral transforms) applied to PDEs |