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1995 On solution of integral equation of Abel-Volterra type
Anatoly A. Kilbas, Megumi Saigo
Differential Integral Equations 8(5): 993-1011 (1995).

Abstract

The linear integral equation of Abel-Volterra type $$ \varphi(x)={\frac{a(x)}{\Gamma(\alpha)}}\int^{x}_{0} {\frac{\varphi(t)}{(x-t)^{1-\alpha}}}\ dt+f(x) \quad (0<x<\infty,\ 0<\alpha <1)\tag{*} $$ is investigated. The asymptotic behavior of the solution $\varphi(x)$ as $x\to 0$ is studied, provided that the functions $a(x)$ and $f(x)$ have special power asymptotic expansions near zero. It is shown that in certain cases such an asymptotic solution $\varphi(x)$ of the equation $(*)$ coincides with its explicit solution. Examples are also given.

Citation

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Anatoly A. Kilbas. Megumi Saigo. "On solution of integral equation of Abel-Volterra type." Differential Integral Equations 8 (5) 993 - 1011, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0823.45002
MathSciNet: MR1325543

Subjects:
Primary: 45M05
Secondary: 45E10

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 5 • 1995
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