scholarly journals Existence of solutions for delay evolution equations with nonlocal conditions

2017 ◽  
Vol 15 (1) ◽  
pp. 616-627 ◽  
Author(s):  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Kuratowski Measure Of Noncompactness

Abstract In this paper, we are devoted to study the existence of mild solutions for delay evolution equations with nonlocal conditions. By using tools involving the Kuratowski measure of noncompactness and fixed point theory, we establish some existence results of mild solutions without the assumption of compactness on the associated semigroup. Our results improve and generalize some related conclusions on this issue. Moreover, we present an example to illustrate the application of the main results.

scholarly journals Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hernán R. Henríquez ◽  
Marcos Rabelo ◽  
Luciana Vale
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Cauchy Problems ◽  
Impulsive Conditions

In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Kexue Li ◽  
Jigen Peng ◽  
Jinghuai Gao
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Kuratowski Measure Of Noncompactness ◽  
Condensing Operator ◽  
Fractional Differential

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.

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 Results for a System of Coupled Hybrid Differential Equations with Fractional Order

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

Existence Results of Mild Solutions for Impulsive Fractional Integrodifferential Evolution Equations With Nonlocal Conditions

2019 ◽  
Vol 20 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Xuping Zhang ◽  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Cosine Family

AbstractIn this paper, we investigate the existence of mild solutions of impulsive fractional integrodifferential evolution equations with nonlocal conditions via the fixed point theorems and fractional cosine family combined with solutions operator theorems. Our results improve and generalize some classical results. Finally, an example is given to illustrate the main results.

scholarly journals Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Integrodifferential Equations

We investigate the existence of solutions for a sequential integrodifferential equation of fractional order with some boundary conditions. The existence results are established by means of some standard tools of fixed point theory. An illustrative example is also presented.

scholarly journals Existence of Solutions for Nonlinear Mixed Type Integrodifferential Functional Evolution Equations with Nonlocal Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Shengli Xie
Keyword(s):  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
A Priori ◽  
Nonlocal Conditions ◽  
Functional Evolution ◽  
Mönch Fixed Point Theorem ◽  
A Priori Estimation

Using Mönch fixed point theorem, this paper proves the existence and controllability of mild solutions for nonlinear mixed type integrodifferential functional evolution equations with nonlocal conditions in Banach spaces, some restricted conditions on a priori estimation and measure of noncompactness estimation have been deleted, our results extend and improve many known results. As an application, we have given a controllability result of the system.

scholarly journals Fractional q-Difference Inclusions in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 91
Author(s):  
Badr Alqahtani ◽  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Sara Salem Alzaid
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Infinite Dimensional ◽  
Difference Inclusions

In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch’s fixed point theorems). Finally we give an illustrative example in the last section. We initiate the study of fractional q-difference inclusions on infinite dimensional Banach spaces.

scholarly journals Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Haide Gou ◽  
Baolin Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Fractional Evolution Equations

We investigate the existence of solutions for a class of impulsive fractional evolution equations with nonlocal conditions in Banach space by using some fixed point theorems combined with the technique of measure of noncompactness. Our results improve and generalize some known results corresponding to those obtained by others. Finally, two applications are given to illustrate that our results are valuable.

Fractional Retarded Evolution Equations with Measure of Noncompactness Subjected to Mixed Nonlocal Plus Local Initial Conditions

2018 ◽  
Vol 19 (1) ◽  
pp. 69-81
Author(s):  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Fixed Point Theory ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Point Theory ◽  
Linear Operators ◽  
Nonlinear Operators ◽  
Bounded Linear ◽  
Uniformly Bounded

AbstractWe consider the fractional retarded evolution equations $$^{C}D_{t}^{q}u(t)+Au(t)=f\Big(t,u_t,\int_{0}^{t}w(t,s,u_s)ds\Big),\quad t\in[0,a],$$where $^{C}D_{t}^{q}$, $q\in(0,1]$, is the fractional derivative in the Caputo sense, $-A$ is the infinitesimal generator of a $C_0$-semigroup of uniformly bounded linear operators $T(t)$$(t\geq0)$ on a Banach space $X$ and the nonlinear operators $f$ and $w$ are given functions satisfying some assumptions, subjected to a general mixed nonlocal plus local initial condition of the form $u(t)=g(u)(t)+\phi(t)$, $t\in[-h,0]$. Under more general conditions, the existence of mild solutions and positive mild solutions are obtained by means of fractional calculus and fixed point theory for condensing maps. Moreover, we present an example to illustrate the application of abstract results.

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