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2020•General Letters in MathematicsOpen access

On Katugampola Laplace transform

Mohammed S. El-Khatib, Tariq O. Salim, Atta A. K. Abu Hany

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Abstract

The aim of this article is to introduce a new form for the Laplace transform. This new definition will be considered as one of the generalizations of the usual (classical) Laplace transform. We employ the new ”Katugampola derivative”, which obeys classical properties and define Katugampola Laplace transform. We obtain some properties of this transform and find the relation between the Katugampola Laplace transform and the usual Laplace one.

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What this paper is about

The aim of this article is to introduce a new form for the Laplace transform. This new definition will be considered as one of the generalizations of the usual (classical) Laplace transform. We employ the new ”Katugampola derivative”, which obeys classical properties and define Katugampola Laplace transform. We obtain some properties of this transform and find the relation between the Katugampola Laplace transform and the usual Laplace one.

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Available abstract

The aim of this article is to introduce a new form for the Laplace transform. This new definition will be considered as one of the generalizations of the usual (classical) Laplace transform. We employ the new ”Katugampola derivative”, which obeys classical properties and define Katugampola Laplace transform. We obtain some properties of this transform and find the relation between the Katugampola Laplace transform and the usual Laplace one.

Key concepts: Laplace transform, Two-sided Laplace transform, Laplace transform applied to differential equations, Post's inversion formula, Laplace–Stieltjes transform, Inverse Laplace transform, Mellin transform, Mathematics

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