Constructing Solutions to Multi-Term Cauchy–Euler Equations with Arbitrary Fractional Derivatives

Autor:	Pavel B. Dubovski, Jeffrey A. Slepoi
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fractional derivative fractional Cauchy–Euler equation characteristic equation Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 13, p 1928 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12131928
Popis:	We further extend the results of other researchers on existence theory to homogeneous fractional Cauchy–Euler equations ∑i=1mdixαiDαiu(x)+μu(x)=0,αi>0, with the derivatives in Caputo or Riemann–Liouville sense. Unlike the existing works, we consider multi-term equations without any restrictions on the order of fractional derivatives. The results are based on the characteristic equations which generate the solutions. Depending on the roots of the characteristic equations (real, multiple, or complex), we construct the corresponding solutions and prove their linear independence.
Databáze:	Directory of Open Access Journals
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