Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 9 (2014), 117 -- 129

EXISTENCE OF MILD SOLUTIONS FOR NONLOCAL CAUCHY PROBLEM FOR FRACTIONAL NEUTRAL EVOLUTION EQUATIONS WITH INFINITE DELAY

V. Vijayakumar, C. Ravichandran and R. Murugesu

Abstract. In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.

2010 Mathematics Subject Classification: 34A08; 34K37; 34K40.
Keywords: fractional neutral evolution equations; nonlocal Cauchy problem; mild solutions; analytic semigroup; Laplace transform; probability density.

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V. Vijayakumar C. Ravichandran
Department of Mathematics, Department of Mathematics,
Info Institute of Engineering, KPR Institute of Engineering and Technology,
Kovilpalayam, Coimbatore-641 107, Arasur, Coimbatore - 641 407,
Tamilnadu, India. Tamilnadu, India.
E-mail: vijaysarovel@gmail.com E-mail: ravibirthday@gmail.com
R. Murugesu
Department of Mathematics,
SRMV College of Arts and Science,
Coimbatore - 641 020,
Tamilnadu, India.
E-mail: arjhunmurugesh@gmail.com

http://www.utgjiu.ro/math/sma