The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces

2010 ◽  
Vol 72 (12) ◽  
pp. 4587-4593 ◽  
Author(s):  
Krishnan Balachandran ◽  
Juan J. Trujillo
Keyword(s):  
Cauchy Problem ◽  
Banach Spaces ◽  
Integrodifferential Equations ◽  
Nonlocal Cauchy Problem

scholarly journals Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

2010 ◽  
Vol 41 (4) ◽  
pp. 361-374
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Cauchy Problem

The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

scholarly journals EXISTENCE OF SOLUTIONS OF SEMILINEAR DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS IN BANACH SPACES

1999 ◽  
Vol 30 (1) ◽  
pp. 21-28
Author(s):  
K. BALACHANDR AN ◽  
M. CHANDRASEKARAN
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Banach Spaces ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Global Solutions ◽  
Contraction Mapping Principle ◽  
Analytic Semigroups ◽  
Nonlocal Cauchy Problem

The aim of this paper is to prove the existence and uniquencess of local, strong and global solutions of a nonlocal Cauchy problem for a differential equation. The method of analytic semigroups and the contraction mapping principle arc used to establish the results.

scholarly journals Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces

2006 ◽  
Vol 37 (3) ◽  
pp. 193-205
Author(s):  
K. Balachandran ◽  
R. Ravikumar
Keyword(s):  
Banach Spaces ◽  
Nonlocal Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Sobolev Type ◽  
Time Varying ◽  
Time Varying Delay ◽  
Compact Semigroups ◽  
Nonlocal Cauchy Problem ◽  
Varying Delay

In this paper we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed point theorem.

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