Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay

2007 ◽  
Vol 67 (4) ◽  
pp. 1027-1041 ◽  
Author(s):  
Abdelghani Ouahab
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Multiple Delay ◽  
Uniqueness Results ◽  
Scalar Multiple ◽  
Functional Differential

scholarly journals Some existence and uniqueness results for first-order boundary value problems for impulsive functional differential equations with infinite delay in Fréchet spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
John R. Graef ◽  
Abdelghani Ouahab
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Fréchet Spaces ◽  
First Order ◽  
Uniqueness Results ◽  
Functional Differential

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas is used to investigate the existence and uniqueness of solutions to first-order boundary value problems for impulsive functional differential equations with infinite delay. An example to illustrate the results is included.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN Lp(Ω, Ch)

2009 ◽  
Vol 09 (04) ◽  
pp. 597-612
Author(s):  
HAIBO BAO ◽  
DAQING JIANG
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we shall consider the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp(Ω, Ch) space: [Formula: see text] where we assume f : R+ × Lp(Ω, Ch) → Lp(Ω, Rn), g : R+ × Lp(Ω, Ch) → Lp(Ω, L(Rm, Rn)), p > 2, and B(t) is a given m-dimensional Brownian motion.

scholarly journals Some Stochastic Functional Differential Equations with Infinite Delay: A Result on Existence and Uniqueness of Solutions in a Concrete Fading Memory Space

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Hassane Bouzahir ◽  
Brahim Benaid ◽  
Chafai Imzegouan
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Fading Memory ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Memory Space ◽  
Functional Differential ◽  
Stochastic Functional

This paper is devoted to existence and uniqueness of solutions for some stochastic functional differential equations with infinite delay in a fading memory phase space.

scholarly journals Results on initial value problems for random fuzzy fractional functional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2601-2624
Author(s):  
Ho Vu ◽  
Ngo Hoa ◽  
Nguyen Son ◽  
Donal O’Regane
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Euler Method ◽  
Successive Approximations ◽  
Initial Value ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

In this paper random fuzzy fractional functional differential equations (RFFFDEs) with Caputo generalized Hukuhara differentiability are introduced. We present existence and uniqueness results for RFFFDEs using the idea of successive approximations. The behaviour of solutions when the data of the equation are subjected to errors is discussed. Furthermore, the solution to random fuzzy fractional functional initial value problem under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method (MFEM) is presented. The results are illustrated with examples.

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