Generalized derivatives and Laplace transform in (k,ψ)-Hilfer form

Başcı Y., MISIR A., Öğrekçi S.

Mathematical Methods in the Applied Sciences, cilt.46, sa.9, ss.10400-10420, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 9
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1002/mma.9129
  • 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.10400-10420
  • Anahtar Kelimeler: (k,Ψ) -Hilfer form, generalized fractional derivatives, generalized fractional integrals, generalized Laplace transforms, k-Mittag-Leffler function, k-Pochhammer symbol
  • Gazi Üniversitesi Adresli: Evet

Özet

In this work, we discuss the most generalized derivatives and integrals and their features in (Formula presented.) -Hilfer form. Furthermore, we define the new generalized Laplace transform to the generalized derivatives and integrals in (Formula presented.) -Hilfer form. Also, we have obtained the new generalized Laplace transforms of some expressions. These statements obtained cover many previous studies. Finally, we have given an example that will both use some of the results obtained and emphasize the importance of parameters such as (Formula presented.), (Formula presented.), (Formula presented.) of the (Formula presented.) -generalized Laplace transform.