scholarly journals Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 927 ◽  
Author(s):  
Akbar Zada ◽  
Shaheen Fatima ◽  
Zeeshan Ali ◽  
Jiafa Xu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Stability Results ◽  
Theoretical Results

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

scholarly journals Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 341 ◽  
Author(s):  
Zeeshan Ali ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Akbar Zada
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
Existence Theory ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Classical Technique ◽  
Fractional Differential ◽  
Stability Results

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

A coupled system of nonlinear differential equations involving m nonlinear terms

2016 ◽  
Vol 23 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Amele Taieb ◽  
Zoubir Dahmani
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Schaefer Fixed Point Theorem ◽  
Fractional Differential ◽  
The Banach Contraction Principle

AbstractIn this paper, we study a coupled system of nonlinear fractional differential equations involving m nonlinear terms, ${m\in\mathbb{N^{*}}}$. We begin by introducing a new Banach space. Then, we establish new existence and uniqueness results using the Banach contraction principle. We also prove an existence result using the Schaefer fixed point theorem. Finally, we give some illustrative 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.

scholarly journals Analysis of a coupled system of fractional differential equations with non-separated boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Danfeng Luo ◽  
Akbar Zada ◽  
Shaleena Shaleena ◽  
Manzoor Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Applied Fields ◽  
Rassias Stability

Abstract Solutions to fractional differential equations is an emerging part of current research, since such equations appear in different applied fields. A study of existence, uniqueness, and stability of solutions to a coupled system of fractional differential equations with non-separated boundary conditions is the main target of this paper. The existence and uniqueness results are obtained by employing the Leray–Schauder fixed point theorem and the Banach contraction principle. Additionally, we examine different types of stabilities in the sense of Ulam–Hyers such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. To prove the effectiveness of our main results, we study a few interesting examples.

scholarly journals A study of a nonlinear coupled system of three fractional differential equations with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bashir Ahmad ◽  
Soha Hamdan ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Coupled System ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractIn this research we introduce and study a new coupled system of three fractional differential equations supplemented with nonlocal multi-point coupled boundary conditions. Existence and uniqueness results are established by using the Leray–Schauder alternative and Banach’s contraction mapping principle. Illustrative examples are also presented.

scholarly journals Stability via successive approximation for nonlinear implicit fractional differential equations

2017 ◽  
Vol 3 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Kishor D. Kucche ◽  
Sagar T. Sutar
Keyword(s):  
Differential Equations ◽  
Successive Approximation ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Stability Results ◽  
Implicit Fractional Differential Equations

Abstract In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

scholarly journals Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
HuiChol Choi ◽  
YongSim Sin ◽  
KumSong Jong
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.

scholarly journals On nonlinear pantograph fractional differential equations with Atangana–Baleanu–Caputo derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed S. Abdo ◽  
Thabet Abdeljawad ◽  
Kishor D. Kucche ◽  
Manar A. Alqudah ◽  
Saeed M. Ali ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence And Uniqueness Results ◽  
Gronwall’S Inequality ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana–Baleanu–Caputo (ABC) derivative operator with fractional orders. Our approach is based on the reduction of FDEs to fractional integral equations and on some fixed point theorems such as Banach’s contraction principle and the fixed point theorem of Krasnoselskii. Further, Gronwall’s inequality in the frame of the Atangana–Baleanu fractional integral operator is applied to develop adequate results for different kinds of Ulam–Hyers stabilities. Lastly, the paper includes an example to substantiate the validity of the results.

scholarly journals On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Guotao Wang ◽  
Bashir Ahmad ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Impulsive Differential Equations ◽  
Irregular Boundary ◽  
Existence And Uniqueness Results ◽  
Impulsive Boundary Value Problems ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Irregular Boundary Conditions

We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

Sign in / Sign up

Export Citation Format

Share Document