On q-Laplace type integral operators and their applications

Abstract

In this work, two q-Laplace type integral transforms called -transform and -transform are introduced. Some properties of q-analogues of the -transform are given, and several relationships between them are studied. Moreover, we show that the new Laplace type q-integral transforms may be regarded as q-extension of the ℒ₂-transform. Some illustrative examples are also given.

Keywords:

• q-calculus
• Jackson integral
• q-Laplace transform
• q-gamma function
• the _q L ₂-transform
• _q L ₂-transform

2000 Mathematics Subject Classification::

• Primary 33D15, 33D60
• Secondary 44A10

Acknowledgements

The authors thank the referee for his/her suggestions, which improved the presentation of this paper. Also, the authors thank Professor S.D. Purohit for his valuable suggestions and criticisms. The present investigation was supported by the Marmara University Scientific Research Project Commission (BAPKO) under Grant 2008 FEN-C-YLP-010508-0101.

Notes

1. [email protected]

Additional information

Notes on contributors

Durmuş Albayrak

1