Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

ALBAYRAK D., DERNEK N.

Gazi University Journal of Science, cilt.36, ss.362-381, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36
  • Basım Tarihi: 2023
  • Doi Numarası: 10.35378/gujs.813138
  • Dergi Adı: Gazi University Journal of Science
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.362-381
  • Anahtar Kelimeler: Laplace transform, Widder Potential transform, Hankel transform, Riemann-Liouville fractional integral, Weylfractionalintegral, IDENTITIES
  • Marmara Üniversitesi Adresli: Evet

Özet

In this paper, Parseval-Goldstein type theorems involving the G(n)-integral transform which is modified from G(2n)-integral transform [7] and the-integral transform [8] are examined. Then, theorems in this paper are shown to yield a number of new identities involving several well-known integral transforms. Using these theorems and their corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Generalizations of Riemann-Liouville and Weyl fractional integral operators are also defined. Some theorems relating generalized Laplace transform, generalized Widder Potential transform, generalized Hankel transform and generalized Bessel transform are obtained. Some illustrative examples are given as applications of these theorems and their results.