Identities for the -transform and their applications

Brown, D. J. A.; Dernek, Neşe; Yürekli, Osman

doi:10.1016/j.amc.2006.09.139

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Cited by 10 publications

(6 citation statements)

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“…where the left-hand side of the above relation is the Widder potential transform of φ(x) [3]. Comparing the above integral with Lemma 4.3, we obtain…”

Section: Solutionmentioning

confidence: 88%

SOLUTION TO SYSTEM OF PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS USING THE $\mathcal{L}_2$-TRANSFORM

Aghili

Ansari

2011

Anal. Appl.

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“…where the left-hand side of the above relation is the Widder potential transform of φ(x) [3]. Comparing the above integral with Lemma 4.3, we obtain…”

Section: Solutionmentioning

confidence: 88%

SOLUTION TO SYSTEM OF PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS USING THE $\mathcal{L}_2$-TRANSFORM

Aghili

Ansari

2011

Anal. Appl.

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“…Subsequently, various Parseval-Goldstein type identities were given in (for example) Brown et al (2007a), Brown et al (2007b), Dernek et al (2007), Glasser (1973), , and for the L 2 -transform. New solutions techniques were obtained for the Bessel differential equation in Yürekli & Wilson (2002) and the Hermite differential equation in Yürekli & Wilson (2003) using this integral transform.…”

Section: Introductionmentioning

confidence: 99%

Identities for the Glasser transform and their applications

Dernek¹,

Dernek²,

Yürekli³

2012

Contemporary Analysis and Applied Mathematics

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In the present paper the authors show that an iteration of the L 2 -transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2 -transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

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“…In the sequence of these integrals, the classical theory of the transform " s 2;1 has recently been investigated by David Brawn, et al in the survey article [8]. However, the generalized theory of this integral has not been explored yet.…”

Section: Introductionmentioning

confidence: 99%

“…The novelty of this extension fulfills when certain spaces of Boehmians are constructed to the given generalized definition. The classical " s 2;1 transform of an ordinary function .x/ is defined by [8] …”

Section: Introductionmentioning

confidence: 99%