The existence and uniqueness of mild solutions for semilinear impulsive neutral fractional integrodifferential equations with nonlocal conditions in the α -norm

2011 ◽  
Author(s):  
Shuo Zhao ◽  
Jun Yang
Keyword(s):  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations

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 The Neutral Stochastic Integrodifferential Equations with Jumps

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Diem Dang Huan
Keyword(s):  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
Initial Value ◽  
Carathéodory Conditions ◽  
Global And Local ◽  
Continuous Dependence Of Solutions

We study the existence and uniqueness of mild solutions for neutral stochastic integrodifferential equations with Poisson jumps under global and local Carathéodory conditions on the coefficients by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value. Finally, an example is provided to illustrate the effectiveness of the obtained results.

Existence and uniqueness of mild solution for fractional integrodifferential equations of neutral type with nonlocal conditions

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Fang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Neutral Type ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations

AbstractIn this paper, we prove the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations of neutral type with nonlocal conditions in a Banach space. New results are obtained by fixed point theorem.

scholarly journals Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xue Wang ◽  
Bo Zhu
Keyword(s):  
Fixed Point ◽  
Resolvent Operator ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Existence Theory ◽  
Nonlocal Initial Conditions

This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.

Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Min Yang ◽  
Qiru Wang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Hilfer Fractional Derivative ◽  
Fractional Evolution Equations ◽  
Noncompact Measure ◽  
The Fixed Point Theorem ◽  
New Criteria

AbstractIn this paper, we consider a class of evolution equations with Hilfer fractional derivative. By employing the fixed point theorem and the noncompact measure method, we establish a number of new criteria to guarantee the existence and uniqueness of mild solutions when the associated semigroup is compact or not.

scholarly journals An Existence Result for Neutral Delay Integrodifferential Equations with Fractional Order and Nonlocal Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Fang Li ◽  
Gaston M. N'Guérékata
Keyword(s):  
Banach Space ◽  
Existence Theorem ◽  
Fractional Order ◽  
Existence Result ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Neutral Delay ◽  
Measures Of Noncompactness ◽  
Condensing Maps

We study the existence of mild solutions of a class of neutral delay integrodifferential equations with fractional order and nonlocal conditions in a Banach spaceX. An existence result on the mild solution is obtained by using the theory of the measures of noncompactness and the theory of condensing maps. Two examples are given to illustrate the existence theorem.

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