TY - JOUR
T1 - Construction and analysis of series solutions for fractional quasi-Bessel equations
AU - Dubovski, Pavel B.
AU - Slepoi, Jeffrey A.
N1 - Publisher Copyright:
© 2022, Diogenes Co.Ltd.
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
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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 -