scholarly journals On coupled systems of fractional impulsive differential equations by using a new Caputo-Fabrizio fractional derivative

2020 ◽  
Vol 24 (2) ◽  
pp. 1-19
Author(s):  
Ahmed Boudaoui ◽  
Abdeldjalil Slama
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Generalized Metric Spaces ◽  
Solution Sets ◽  
Fixed Point Approach

In this paper, we investigate the existence and uniqueness of solutions for coupled system of Caputo-Fabrizio fractional impulsive differential equations using the fixed point approach in generalized metric spaces. The compactness of solution sets of the system is also investigated. An example is provided to illustrate the developed theory.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

scholarly journals EXISTENCE AND UNIQUENESS RESULTS FOR A COUPLED SYSTEM OF HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS

2020 ◽  
pp. 843
Author(s):  
Mohamed Houas ◽  
Khellaf Ould Melha
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

A Study of Coupled Systems of ψ-Hilfer Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Ayub Samadi ◽  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated. The presented results are obtained via the classical Banach and Krasnosel’skiĭ’s fixed point theorems and the Leray–Schauder alternative. Examples are included to illustrate the effectiveness of the obtained results.

scholarly journals Remark on Existence and Uniqueness of Solutions for a Coupled System of Multiterm Nonlinear Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Huichao Zou ◽  
Yonghong Fan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Function Classes ◽  
Fractional Differential

The aim of this paper is to extend the work of Sun et al. (2012) to a more general case for a wider range of function classes offandg. Our results include the case of the previous work, which are essential improvement of the work of Sun et al. (2012), especially.

scholarly journals Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hojjat Afshari ◽  
Hossein Hosseinpour ◽  
H. R. Marasi
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Metric Spaces ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Contraction Mappings

AbstractIn this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete $\mathfrak{F}$ F -metric spaces for this purpose.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR STOCHASTIC IMPULSIVE DIFFERENTIAL EQUATIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 375-383 ◽  
Author(s):  
LIJUAN SHEN ◽  
JITAO SUN
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Uniqueness Of Solutions ◽  
Special Requirement ◽  
Impulsive Function

This paper is concerned with the existence and uniqueness of solutions for stochastic impulsive differential equations. Some sufficient conditions are obtained by using the notion of measure of noncompactness and the Leray–Schauder type fixed theorem. Since the conditions do not need special requirement of the impulsive function, the results we obtained is more reflexible. An example will illustrate the effectiveness.

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