The qq-analogue of the E2;1E2;1-transform and its applications

In this paper, we introduce a new integral transform qE2;1 , which is the q -analogue of the E2;1 -transform and can be regarded as a q -extension of the E2;1 -transform. Some identities involving qL2 -transfom, qL2 -transfom, and Pq -transform are given. By making use of these identities and qE2;1 -transform, a new Parseval Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.

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[1] Albayrak D, Purohit SD, U¸car F. On q -integral transforms and their applications. Bulletin of Mathematical Analysis and Applications 2012; 4: 103-115.
[2] Brown D, Dernek N, Y¨urekli O. Identities for the E2;1 -transform and their applications. Appl Math Comput 2007; 187: 1557-1566.
[3] El-Shahed M, Salem A. On q -analogue of the incomplete gamma function. Int J Pure Appl Math 2008; 44: 773-780.
[4] K¨urem G, Vula¸s B. q -Laplace transforms. Proceedings of the Jangjeon Mathematical Society 2009; 12: 203-218.
[5] Salem A. A q -analogue of the exponential integral. Afrika Matematika 2013; 24: 117-125.
[6] U¸car F, Albayrak D. On q -Laplace type integral operators and their applications. J Differ Equ Appl 2012; 18: 1001-1014.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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