Advances in Laplace Type Integral Transforms with Applications

A  Aghili  and H  Zeinali

doi:10.17485/ijst/2014/v7i6.20

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Advances in Laplace Type Integral Transforms with Applications

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2014/v7i6.20

Year: 2014, Volume: 7, Issue: 6, Pages: 877–890

Original Article

Advances in Laplace Type Integral Transforms with Applications

A. Aghili^* and H. Zeinali

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O.Box, 1841, Rasht, Iran; arman.aghili@gmail.com, homa_zeinaly@yahoo.com

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In this study, the authors implemented one and two dimensional Laplace transform, Stieltjes and Post-Widder transforms to evaluate certain integrals and series. In the last section, certain fractional wave equation is solved via joint Laplace– Fourier sine transform. Illustrative examples are also provided. The result reveals that the integral transform method performs extremely well in terms of simplicity and efficiency. Mathematics Subject Classification 2010: 26A33; 34A08; 34K37; 35R11.
Keywords: Bessel’s Functions, Mathieu Series, Post-Widder transform, Two Dimensional Laplace Transform, Stieltjes Transform