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

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

doi:10.17485/ijst/2015/v8i4/67385

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

S. Manimaran ¹, T. Gunasekar ², G. V. Subramaniyan ³, F. Paul Samuel ⁴

Affiliations
1 Ramakrishna Mission Vivekananda College, Chennai-600 004, Tamil Nadu, India
2 School of Advanced Sciences, Fluid Dynamics Division, VIT University, Vellore-632 014, Tamil Nadu, India
3 Department of Mathematics, Sudharshan College of Engineering, Sathiyamangalam, Pudukkottai-622 001, Tamil Nadu, India
4 Department of Mathematics and Physics, University of Eastern Africa, Baraton, Eldoret 2500-30100, Kenya

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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.