Theory and applications on a new generalized Laplace-type integral transform

ALBAYRAK D.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.46, sa.4, ss.4363-4378, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1002/mma.8763
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.4363-4378
  • Anahtar Kelimeler: convolution, differential equations, integral equations, Laplace transform, partial differential equations
  • Marmara Üniversitesi Adresli: Evet

Özet

In this paper, several theorems and relations are examined by using a generalized Laplace-type integral transform. A generalization of the harmonic oscillator in a non-resisting and resisting medium problems, initial-boundary problems, and integral equations is solved via this integral transform. Furthermore, the well-known series entitled as Basel problem is obtained in a similar way. Moreover, we compare numerically classical and newly introduced by us integral transform.