Construction and analysis of series solutions for fractional quasi-Bessel equations

Pavel B. Dubovski, Jeffrey A. Slepoi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we introduce fractional quasi-Bessel equations ∑i=1mdixξiDαiu(x)+(xβ-ν2)u(x)=0and construct their existence theory in the class of fractional series solutions. In order to find the parameters of the series, we derive the characteristic equation, which is surprisingly independent of the terms with non-matching parameters ξi≠ αi. Our methodology allows us to obtain new results for a broad class of fractional differential equations including quasi-Euler equations. As a particular example, we demonstrate how our approach works for the constant-coefficient equations. The theoretical results are justified computationally.

Original languageEnglish
Pages (from-to)1229-1249
Number of pages21
JournalFractional Calculus and Applied Analysis
Volume25
Issue number3
DOIs
StatePublished - Jun 2022

Keywords

  • Blow-up of solutions
  • Cauchy-Euler equations
  • Constant-coefficient equations
  • Existence
  • Fractional calculus
  • Fractional differential equations
  • Fractional power series
  • Mittag-Leffler functions
  • Quasi-Bessel equations
  • Quasi-Euler equations

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