On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions

2004 ◽  
pp. 1-11 ◽  
Author(s):  
Haydar Akça ◽  
Valéry Covachev ◽  
Eada Al-Zahrani
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Functional Differential

A class of fractional impulsive functional differential equations with nonlocal conditions

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Yiliang Liu ◽  
Jiangfeng Han
Keyword(s):  
Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Functional Differential

AbstractIn this paper, we deal with the existence of solutions for the fractional impulsive functional differential equations with nonlocal conditions. Then we build a new comparison theorem and obtain the existence of extremal solutions and quasi-solutions by use of the monotone iterative technique and the method of lower and upper solutions.

scholarly journals On nondensely defined semilinear stochastic functional differential equations with nonlocal conditions

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas ◽  
A. Ouahab
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Stochastic Functional Differential Equations ◽  
First Order ◽  
Nonlinear Alternative ◽  
Functional Differential ◽  
Stochastic Functional

The nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first-order semilinear stochastic functional differential equations in Hilbert spaces.

Solutions to fractional functional differential equations with nonlocal conditions

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Shruti Dubey ◽  
Madhukant Sharma
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Classical Solutions ◽  
Operator Family ◽  
Order Partial Differential Equation ◽  
Lipschitz Continuous ◽  
Nonlinear Part ◽  
Functional Differential

AbstractIn this paper, we discuss the solutions to nonlocal initial value problems of fractional order functional differential equations in a Banach space. In particular, we prove the existence and uniqueness of mild and classical solutions assuming that −A generates a resolvent operator family and nonlinear part is a Lipschitz continuous function. We also investigate the global existence of the solution. At the end, a fractional order partial differential equation is given to illustrate the obtained abstract results.

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