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

Pavel B. Dubovski, Jeffrey A. Slepoi

Research output: Contribution to journalArticlepeer-review

Abstract

We further extend the results of other researchers on existence theory to homogeneous fractional Cauchy–Euler equations (Formula presented.) 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.

Original languageEnglish
Article number1928
JournalMathematics
Volume12
Issue number13
DOIs
StatePublished - Jul 2024

Keywords

  • characteristic equation
  • fractional Cauchy–Euler equation
  • fractional derivative

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