Communications in Mathematical Analysis

Existence of Mild Solutions for Nonlocal Cauchy Problem for Fractional Neutral Integro-Differential Equation with Unbounded Delay

R. Murugesu, V. Vijayakumar, and J. P. C. dos Santos

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Abstract

In this article, we study the existence of mild solutions for the nonlocal Cauchy problem for a class of abstract fractional neutral integro-differential equations with infinite delay. The results are obtained by using the theory of resolvent operators. Finally, an application is given to illustrate the theory.

Article information

Source
Commun. Math. Anal., Volume 14, Number 1 (2013), 59-71.

Dates
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.cma/1364216230

Mathematical Reviews number (MathSciNet)
MR3040881

Zentralblatt MATH identifier
1283.34071

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
Secondary: 35R10: Partial functional-differential equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Keywords
Fixed point metric space binary relation ordered set cyclical mappings

Citation

dos Santos, J. P. C.; Vijayakumar, V.; Murugesu, R. Existence of Mild Solutions for Nonlocal Cauchy Problem for Fractional Neutral Integro-Differential Equation with Unbounded Delay. Commun. Math. Anal. 14 (2013), no. 1, 59--71. https://projecteuclid.org/euclid.cma/1364216230


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