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, vol.72, no.2, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.24425/bpasts.2024.149170
  • Journal Name: BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES
  • Journal Indexes: 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
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

We introduce the Sobolev-type multi -term mu-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.