Existence and linear independence theorem for linear fractional differential equations with constant coefficients

• Autorzy: Dubovski Pavel B. , Slepoi Jeffrey A.

Identyfikatory

DOI

10.1515/jaa-2023-0009

• Języki publikacji: EN

Abstrakty

EN

We consider the l-th order linear fractional differential equations with constant coefficients. Here l ∈ ℕ is the ceiling for the highest derivative of order α, l − 1 < α ≤ l. If βi < α are the other derivatives, the existing theory requires α − max{βi} ≥ l − 1 for the existence of l linearly independent solutions. Thus, at most one derivative may have order greater than one, but all other derivatives must be between zero and one. We remove this essential restriction and construct l linearly independent solutions. With this aim, we remodel the series approaches and elaborate the multi-sum fractional series method in order to obtain the existence and linear independence results.We consider both Riemann-Liouville or Caputo fractional derivatives.

Słowa kluczowe

PL

constant-coefficient fractional differential equations; multi-sum fractional series; double fractional series; linear independence

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2024
• Tom: Vol. 30, nr 1
• Strony: 117--128
• Opis fizyczny: Bibliogr. 23 poz., wykr.

Twórcy

autor

Dubovski Pavel B.

• Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA

• https://orcid.org/0000-0002-5070-2911

autor

Slepoi Jeffrey A.

• Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).