Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators

2010 ◽  
Vol 4 (1) ◽  
pp. 32-43 ◽  
Author(s):  
Y.-K. Chang ◽  
V. Kavitha ◽  
M. Mallika Arjunan
Keyword(s):  
Nonlocal Conditions ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Fractional Operators

scholarly journals Existence results for some partial integrodifferential equations with nonlocal conditions

2016 ◽  
Vol 51 (2) ◽  
pp. 413-430 ◽  
Author(s):  
Khalil Ezzinbi ◽  
◽  
Saifeddine Ghnimi ◽  
Mohamed-Aziz Taoudi ◽  
◽  
...  
Keyword(s):  
Nonlocal Conditions ◽  
Existence Results ◽  
Integrodifferential Equations

scholarly journals Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Dang Huan Diem
Keyword(s):  
Infinite Delay ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Bounded Linear ◽  
Infinite Delays ◽  
Strongly Continuous Cosine Family

The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given.

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

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