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.

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.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 630
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Nonlinear Alternative ◽  
Contractive Map ◽  
Fractional Differential ◽  
Definition Of

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

scholarly journals Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Control Systems ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Fractional Differential

We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce thePC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.

scholarly journals Existence results for fractional integro-differential inclusions with state-dependent delay

2017 ◽  
Vol 4 (1) ◽  
pp. 62-77
Author(s):  
Giovana Siracusa ◽  
Hernán R. Henríquez ◽  
Claudio Cuevas
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Existence Results ◽  
Materials With Memory ◽  
State Dependent ◽  
State Dependent Delay ◽  
Contractive Maps ◽  
Infinite State ◽  
With Memory ◽  
Condensing Maps

AbstractIn this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

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.

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