ON GENERALIZED STIELTJES-TYPE INTEGRAL TRANSFORM: THEORY AND APPLICATIONS

Salimov R., ALBAYRAK D.

Journal of Mathematical Sciences (United States), 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s10958-025-07864-4
  • Dergi Adı: Journal of Mathematical Sciences (United States)
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Convolution, Generalized laplace-type transform, Generalized stieltjes transform, Generalized stieltjes-type transform, Integral transform, Laplace transform, Stieltjes transform
  • Marmara Üniversitesi Adresli: Evet

Özet

This paper is focused on the generalized Stieltjes-type integral transform. We derive the transform of a specific derivative operator and also achieve the transforms of integrals and fractional integrals. A significant contribution of this paper is the introduction of a new convolution associated with this transform, along with a proof of the corresponding convolution theorem. Additionally, the transform is employed to solve a variety of problems, including initial-boundary value problems for both ordinary and partial differential equations, as well as an integral equation.