Darboux problem for perturbed hyperbolic differential inclusions with fractional order

2019 ◽  
Vol 39 (1) ◽  
pp. 53
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Differential Inclusions ◽  
Darboux Problem ◽  
Hyperbolic Differential Inclusions

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.

APPROXIMATION OF HYPERBOLIC DIFFERENTIAL INCLUSIONS OF FRACTIONAL ORDER WITH IMPULSES

2018 ◽  
pp. 738-744
Author(s):  
Victor Victorovich Skomorokhov
Keyword(s):  
Approximate Solution ◽  
Differential Inclusion ◽  
Fractional Order ◽  
Differential Inclusions ◽  
External Disturbance ◽  
Asymptotic Properties ◽  
Hyperbolic Differential Inclusion ◽  
Hyperbolic Differential Inclusions

In this paper there are considered hyperbolic differential inclusions of fractional order with impulses. Here we represent the concept of approximate solution (δ-solution) for a hyperbolic differential inclusion of fractional order with impulses. The asymptotic properties of solutions sets to approximating differential inclusions of fractional order with external disturbance are derived.

scholarly journals Impulsive partial hyperbolic differential inclusions of fractional order

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Hyperbolic Differential Inclusions

AbstractIn this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

scholarly journals Controllability results for fractional order neutral functional differential inclusions with infinite delay

2017 ◽  
Vol 18 (2) ◽  
pp. 773-798 ◽  
Author(s):  
Yong Zhou ◽  
◽  
V. Vijayakumar ◽  
C. Ravichandran ◽  
R. Murugesu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Differential Inclusions ◽  
Infinite Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

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 Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 422 ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Pharunyou Chanthorn ◽  
Pramet Kaewmesri ◽  
Ramalingam Sriraman ◽  
Chee Peng Lim
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
State Feedback ◽  
Control Law ◽  
Memristive Neural Networks ◽  
Numerical Examples ◽  
Quaternion Multiplication ◽  
Stabilizing Control ◽  
Stability And Stabilization

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

Sign in / Sign up

Export Citation Format

Share Document