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

Pavel B. Dubovski; Jeffrey A. Slepoi

doi:10.1007/s13540-022-00045-z

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

Pavel B. Dubovski
, Jeffrey A. Slepoi

Department of Mathematical Sciences

Stevens Institute of Technology

Research output: Contribution to journal › Article › peer-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 ξ_i≠ α_i. 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 language	English
Pages (from-to)	1229-1249
Number of pages	21
Journal	Fractional Calculus and Applied Analysis
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s13540-022-00045-z
State	Published - 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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10.1007/s13540-022-00045-z

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title = "Construction and analysis of series solutions for fractional quasi-Bessel equations",

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.",

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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doi = "10.1007/s13540-022-00045-z",

language = "English",

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TY - JOUR

T1 - Construction and analysis of series solutions for fractional quasi-Bessel equations

AU - Dubovski, Pavel B.

AU - Slepoi, Jeffrey A.

PY - 2022/6

Y1 - 2022/6

N2 - 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.

AB - 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.

KW - Blow-up of solutions

KW - Cauchy-Euler equations

KW - Constant-coefficient equations

KW - Existence

KW - Fractional calculus

KW - Fractional differential equations

KW - Fractional power series

KW - Mittag-Leffler functions

KW - Quasi-Bessel equations

KW - Quasi-Euler equations

UR - https://www.scopus.com/pages/publications/85132584530

UR - https://www.scopus.com/pages/publications/85132584530#tab=citedBy

U2 - 10.1007/s13540-022-00045-z

DO - 10.1007/s13540-022-00045-z

M3 - Article

AN - SCOPUS:85132584530

SN - 1311-0454

VL - 25

SP - 1229

EP - 1249

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 3

ER -

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

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