scholarly journals Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay

2006 ◽  
Vol 323 (1) ◽  
pp. 456-472 ◽  
Author(s):  
Abdelghani Ouahab
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Multiple Delay ◽  
Uniqueness Results ◽  
Global Existence And Uniqueness ◽  
Functional Differential

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.

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.

Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations

2002 ◽  
Vol 9 (3) ◽  
pp. 423-430
Author(s):  
M. Benchohra ◽  
A. Ouahabi
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Functional Differential ◽  
The Banach Contraction Principle

Abstract The Banach contraction principle is used to investigate the existence and uniqueness of solutions for first and second order impulsive semilinear neutral functional differential equations in Banach spaces.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

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