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2012•ISRN Applied MathematicsOpen access

New Inversion Techniques for Some Integral Transforms via the Generalized Product Theorem of the Mellin Transform

Alireza Ansari, Mohammadreza Ahmadi Darani

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Abstract

We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem. Also, new inversion techniques for the Wright, Mittag-Leffler, Stieltjes, and Widder potential transforms are obtained.

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We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem. Also, new inversion techniques for the Wright, Mittag-Leffler, Stieltjes, and Widder potential transforms are obtained.

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Available abstract

We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem. Also, new inversion techniques for the Wright, Mittag-Leffler, Stieltjes, and Widder potential transforms are obtained.

Key concepts: Mellin transform, Mellin inversion theorem, Two-sided Laplace transform, Integral transform, Mathematics, Inversion (geology), Product (mathematics), Laplace transform

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