Existence and uniqueness of mild solutions for fractional integrodifferential equations with nonlocal conditions in Banach spaces

2014 ◽  
Vol 8 ◽  
pp. 369-379
Author(s):  
V. Dhanapalan ◽  
M. Thamilselvan ◽  
M. Chandrasekaran
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations

scholarly journals On Existence and uniqueness to solutions nonlocal integrodifferential equations

2018 ◽  
Vol 1 (25) ◽  
pp. 493-508
Author(s):  
Fawzi Mutter Ismaael
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem

The Study aims in this paper to give and investigate the existence and uniqueness of mild solutions to nonlinear functional integrodifferential equations in Banach Spaces. the fixed point theorem, according to Sadovskii and sutible necessary conditions, are concepts consulted to obtain the results in the work

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

scholarly journals On solutions of semilinear evolution integrodifferential equations with nonlocal conditions

2009 ◽  
Vol 40 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Theory Of Evolution ◽  
Banach’S Contraction Principle

In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.

scholarly journals Instantaneous and Noninstantaneous Impulsive Integrodifferential Equations in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Gaston M. N'Guérékata
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
The Resolvent Operator

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.

scholarly journals Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1133-1149
Author(s):  
S. Marshal Anthoni ◽  
J.-H. Kim ◽  
J. P. Dauer
Keyword(s):  
Banach Spaces ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.

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