The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay

2010 ◽  
Vol 4 (4) ◽  
pp. 775-781 ◽  
Author(s):  
Xianmin Zhang ◽  
Xiyue Huang ◽  
Zuohua Liu
Keyword(s):  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Fractional Equations

scholarly journals Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Jaydev Dabas ◽  
Archana Chauhan ◽  
Mukesh Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Fractional Equations ◽  
Evolution Differential Equation

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

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.

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 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.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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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