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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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

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

First available in Project Euclid: 25 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Fixed point metric space binary relation ordered set cyclical mappings


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.

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