Journal of Integral Equations and Applications

Application of a global implicit function theorem to a general fractional integro-differential system of Volterra type

Dariusz Idczak and Stanislaw Walczak

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Abstract

In this paper, we use a global implicit function theorem for the investigation of the existence and uniqueness of a solution as well as the sensitivity of a Cauchy problem for a general integro-differential system of order $\alpha \in (0,1)$ of Volterra type, involving two functional parameters nonlinearly.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 4 (2015), 521-554.

Dates
First available in Project Euclid: 8 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1454939252

Digital Object Identifier
doi:10.1216/JIE-2015-27-4-521

Mathematical Reviews number (MathSciNet)
MR3457681

Zentralblatt MATH identifier
1334.26009

Subjects
Primary: 26A33: Fractional derivatives and integrals 34K37: Functional-differential equations with fractional derivatives 47J07: Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]

Keywords
Fractional derivatives integro-differential equations sensitivity global implicit function theorem

Citation

Idczak, Dariusz; Walczak, Stanislaw. Application of a global implicit function theorem to a general fractional integro-differential system of Volterra type. J. Integral Equations Applications 27 (2015), no. 4, 521--554. doi:10.1216/JIE-2015-27-4-521. https://projecteuclid.org/euclid.jiea/1454939252


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