scholarly journals Generalized functional differential equations: existence and uniqueness of solutions

2016 ◽  
pp. 1-19
Author(s):  
Arkadi Ponosov ◽  
Evgeny Zhukovskiy
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Functional Differential

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 Functional Differential Equations Involving the ψ-Caputo Fractional Derivative

2020 ◽  
Vol 4 (2) ◽  
pp. 29
Author(s):  
Ricardo Almeida
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Arbitrary Function ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Derivative Operator ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

This paper is devoted to the study of existence and uniqueness of solutions for fractional functional differential equations, whose derivative operator depends on an arbitrary function. The introduction of such function allows generalization of some known results, and others can be also obtained.

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