scholarly journals Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
A. Vinodkumar ◽  
A. Boucherif
Keyword(s):  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
A Priori ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
A Priori Bounds ◽  
Stochastic Differential Inclusions ◽  
Multivalued Operators

We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.

scholarly journals On a nonlocal Cauchy problem for differential inclusions

2004 ◽  
Vol 2004 (5) ◽  
pp. 425-434 ◽  
Author(s):  
E. Gatsori ◽  
S. K. Ntouyas ◽  
Y. G. Sficas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Nonlocal Cauchy Problem

We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.

scholarly journals Existence Results for Semilinear Functional Differential System with Nonlocal Conditions

2018 ◽  
Vol 8 (10S) ◽  
pp. 237-241
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Abstract Space ◽  
Functional Differential ◽  
Functional Differential System

In this paper, sufficient conditions are given for the existence of partial functional differential equations with nonlocal conditions in an abstract space with the help of the fixed point theorems.

scholarly journals Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed Gamal Ibrahim ◽  
Donal O’Regan
Keyword(s):  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Continuous Functions ◽  
Sobolev Type ◽  
Unbounded Interval ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory, multi-functions and a measure of noncompactness on the space of piecewise weighted continuous functions defined on an unbounded interval. An example is provided to illustrate our results.

scholarly journals Existence of Mild Solutions for Impulsive Fractional Stochastic Differential Inclusions with State-Dependent Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Toufik Guendouzi ◽  
Ouahiba Benzatout
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
State Dependent ◽  
Nonlinear Alternative ◽  
Stochastic Differential Inclusions ◽  
State Dependent Delay

We study the existence of mild solutions for a class of impulsive fractional stochastic differential inclusions with state-dependent delay. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O’Regan. An example is given to illustrate the theory.

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 New results on Caputo fractional-order neutral differential inclusions without compactness

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
C. Ravichandran ◽  
Thabet Abdeljawad ◽  
N. Valliammal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Order ◽  
Weak Topology ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Neutral System

AbstractThis article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

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.

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

Semilinear fractional order integro-differential inclusions with infinite delay

2018 ◽  
Vol 25 (3) ◽  
pp. 317-327 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Banach Spaces ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Nonlinear Alternative

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

Sign in / Sign up

Export Citation Format

Share Document