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

• Autorzy: Aydin Mustafa , Mahmudov Nazim I.

Identyfikatory

DOI

10.24425/bpasts.2024.149170

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

degenerate evolution equation; Sobolev; generalized Laplace transform; fractional derivative with respect to another function; Mittag-Leffler type function

PL

Sobolew; pochodna ułamkowa względem innej funkcji; funkcja typu Mittaga-Lefflera; uogólniona transformata Laplace'a; równanie ewolucji zdegenerowane

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2024
• Tom: Vol. 72, nr 2
• Strony: art. no. e149170
• Opis fizyczny: Bibliogr 28 poz.

Twórcy

autor

Aydin Mustafa

• Department of Medical Services and Techniques, Muradiye Vocational School, Van Yuzuncu Yil University, Tuşba 65080 Van, Turkey

• https://orcid.org/0000-0003-0132-9636

autor

Mahmudov Nazim I.

• Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Turkey
• Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan

• https://orcid.org/0000-0003-3943-1732

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).