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A generalized Sumudu transform. (English) Zbl 1218.44001

An integral transform, called the Sumudu transform was defined and studied by G. K. Watugala [ Math. Eng. Ind. 6, No. 4, 319–329 (1998; Zbl 0916.44002)]. Units and scale preserving properties make the Sumudu transform an ideal tool for solving many engineering problems without restoring to a new frequency domain. In this paper, by observing that the Sumudu transform \(G\) and the Laplace transform \(F\) satisfies the relationship \(G(u)=\frac 1u F(\frac 1u)\), the authors mention some properties of the Sumudu transform and then introduce a new generalized transform involving confluent hypergeometric function as kernel. Some properties of this new transform are established and images of certain special functions, including Mittag-Leffler and H-functions, under this transform are given. An inversion formula for this transform is also obtained, by using Laplace and its inverse operators.

MSC:

44A20 Integral transforms of special functions
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33E12 Mittag-Leffler functions and generalizations
35A22 Transform methods (e.g., integral transforms) applied to PDEs

Citations:

Zbl 0916.44002
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