Existence of Solutions for Neutral Functional Integrodifferential Evolution Equations with Non Local Conditions

S  Manimaran; T  Gunasekar; G  V  Subramaniyan  and F  Paul Samuel

doi:10.17485/ijst/2015/v8i4/60133

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Existence of Solutions for Neutral Functional Integrodifferential Evolution Equations with Non Local Conditions

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i4/60133

Year: 2015, Volume: 8, Issue: 4, Pages: 358–363

Original Article

Existence of Solutions for Neutral Functional Integrodifferential Evolution Equations with Non Local Conditions

S. Manimaran¹ , T. Gunasekar^2* , G. V. Subramaniyan³ and F. Paul Samuel⁴

¹Ramakrishna Mission Vivekananda College, Chennai - 600 004, Tamil Nadu, India; ponsumanimaran@gmail.com

²School of Advanced Sciences, Fluid Dynamics Division, VIT University, Vellore - 632 014, Tamil Nadu, India; gunasekar.t@vit.ac.in

³Department of Mathematics, Sudharshan College of Engineering, Sathiyamangalam, Pudukkottai - 622 001, Tamil Nadu, India; tguna84@gmail.com 4 Department of Mathematics and Physics, University of Eastern Africa, Baraton, Eldoret 2500 - 30100, Kenya; paulsamuelphd@yahoo.com

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

We study the existence of mild and strong solutions for nonlinear neutral functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. The results are obtained by using the fractional powers of operators and Sadovskii’s fixed point theorem.

Keywords:
Mild and Strong Solution, Neutral Equations, Nonlocal Condition, Semigroup