|
|
 |
| |
|
|
|
New Perspectives of the Lambert-Widder Transform: Singular Non-Local Operators with Exponential Memory |
|
|
|
PP: 547-584 |
|
|
|
doi:10.18576/pfda/110309
|
|
|
|
Author(s) |
|
|
|
Jordan Hristov,
|
|
|
|
Abstract |
|
|
| The Lambert-Widder transform has been seen from a different angle while formulating novel non-local singular operators that possess exponential memory. An extensive examination of the basic singular version of the Lambert-Widder kernel by a transformation toward a memory function in a convolution integral controlled by a fractional parameter has been thoroughly carried out. The kernel monotonicity analysis, its Mellin transform, and consequent formulations of novel fractional integral and fractional derivative have been carried out. Examples of formal differential and integral equations involving the novel operators possessing the Mellin transform have been formulated. The application of the fading memory approach demonstrates a build-up of a heat conduction model with a memory integral involving the Lambert-Widder kernel. Some extensions of the new operator based on the Mittag-Leffler function are suggested.
|
|
|
|
|
|
|
|
