Some Results on the Generalized Mellin Transforms and Applications

Year 2019, Volume: 7 Issue: 1, 175 - 181, 15.04.2019

Ezgi Erdoğan Selcan Kocabaş Nese Dernek

Abstract

This paper
discusses the generalized Mellin transforms and their properties with examples
and applications to integral and partial differential equations. Several simple
lemmas and theorems dealing with general properties of the generalized Mellin
transform are proved. The main focus of this paper is to develop the method of
the generalized Mellin transform to solve partial differential equations and
integral equations in applied mathematics.

Keywords

Fourier transforms, Mellin transforms, generalized Mellin transforms, integral, partial differential equations

References

• [1] D. Brown, N. Dernek and O. Yürekli, Identities for the L2;1 Transform and Their Applications, Appl. Math. Comput., 187, (2007), 1557-1566.
• [2] L. Debnath, D. Bhatta, Integral Transforms and Their Applications Second Edition, Chapman&Hall, 2006.
• [3] L. Debnath, The Double Laplace Transforms and Their Properties with Applications to Functional, Integral and Partial Differential Equations, Int. J. Appl. Comput. Math., 2 (2016), 223-241.
• [4] N. Dernek, F. Aylıkçıand O. Yürekli, New Identities on the Generalized Exponential and Mellin Integral transformatons and Their Applications(to appear)
• [5] N. Dernek, F. Aylıkçı and S. Kıvrak, An Alternative Technique for Solving Ordinary Differential Equations, Konuralp J. Math., Vol 4:1 (2016), 68-79.
• [6] A. Erdelyi, W. Magnus, F. Oberhettinger, and G. Tricomi, Tables of Integral Transforms, Vol. I, Vol. II, New York: McGraw Hill, 1954.
• [7] N. Lebedev, Special Functions and Their Applications, Prentice Hall, 1965.