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.

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.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

2003 ◽  
Vol 13 (06) ◽  
pp. 807-841 ◽  
Author(s):  
R. Ouifki ◽  
M. L. Hbid
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Delay Equation ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

scholarly journals Existence and Uniqueness Results for a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

2020 ◽  
Vol 4 (2) ◽  
pp. 13 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

scholarly journals Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zihan Gao ◽  
Tianlin Hu ◽  
Huihui Pang
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Continuous Operator ◽  
Impulsive Effect ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Multiple Band ◽  
Fractional Differential

In this paper, we consider a class of nonlinear Caputo fractional differential equations with impulsive effect under multiple band-like integral boundary conditions. By constructing an available completely continuous operator, we establish some criteria for judging the existence and uniqueness of solutions. Finally, an example is presented to demonstrate our main results.

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

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