scholarly journals The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Bouchra Ben Amma ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Parametric Problem ◽  
Partial Functional Differential Equations ◽  
Intuitionistic Fuzzy ◽  
Functional Differential ◽  
Fuzzy Solutions

In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence and uniqueness of the solution. An example is presented to illustrate the results with some numerical simulation for α-cuts of the intuitionistic fuzzy solutions: we give the representation of the surface of intuitionistic fuzzy solutions.

scholarly journals Faedo-Galerkin approximation of mild solutions of fractional functional differential equations

2021 ◽  
Vol 8 (1) ◽  
pp. 1-17
Author(s):  
J. Vanterler da C. Sousa ◽  
Michal Fečkan ◽  
E. Capelas de Oliveira
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Galerkin Approximation ◽  
Banach Fixed Point Theorem ◽  
Convergence Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

Abstract In the paper, we discuss the existence and uniqueness of mild solutions of a class of fractional functional differential equations in Hilbert space separable using the Banach fixed point theorem technique. In this sense, Faedo-Galerkin approximation to the solution is studied and demonstrated some convergence results.

scholarly journals On State-Dependent Delay Intuitionistic Fuzzy Partial Functional Differential Equations with Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Bouchra Ben Amma ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Intuitionistic Fuzzy ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Fuzzy Solutions

This paper addresses the issue of the existence and uniqueness of intuitionistic fuzzy solutions for some classes of partial functional differential equations with state-dependent delay in a new weighted complete metric space. Theorems on the existence and uniqueness of intuitionistic fuzzy solutions for these problems with integral boundary conditions are established under some sufficient assumptions. Some numerical examples of applications of the main result of this work are presented.

Fuzzy Solutions for Neutral Functional Differential Equations with Nonlocal Conditions

2004 ◽  
Vol 11 (1) ◽  
pp. 35-42
Author(s):  
Amaria Arara ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fuzzy Solutions

Abstract The Banach fixed point theorem is used to investigate the existence of fuzzy solutions for first and second order neutral functional differential equations with nonlocal conditions.

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