Some applications of the generalized Laplace transform and the representation of a solution to Sobolev-type evolution equations with the generalized Caputo derivative

Aydın M., Mahmudov N. I.

Bulletin of the Polish Academy of Sciences: Technical Sciences, cilt.72, sa.2, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.24425/bpasts.2024.149170
  • Dergi Adı: Bulletin of the Polish Academy of Sciences: Technical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: degenerate evolution equation, fractional derivative with respect to another function, generalized Laplace transform, Mittag-Leffler type function., Sobolev
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We introduce the Sobolev-type multi-term μ-fractional evolution with generalized fractional orders with respect to another function. We make some applications of the generalized Laplace transform. In the sequel, we propose a novel type of Mittag-Leffler function generated by noncommutative linear bounded operators with respect to the given function and give a few of its properties. We look for the mild solution formula of the Sobolev-type evolution equation by building on the aforementioned Mittag-Leffler-type function with the aid of two different approaches. We share new special cases of the obtained findings.