scholarly journals New results for a coupled system of ABR fractional differential equations with sub-strip boundary conditions

2021 ◽  
Vol 7 (3) ◽  
pp. 4386-4404
Author(s):  
Mohammed A. Almalahi ◽  
◽  
Satish K. Panchal ◽  
Tariq A. Aljaaidi ◽  
Fahd Jarad ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Alternative Theorem ◽  
Fractional Differential ◽  
Mathematical Techniques ◽  
The Stability ◽  
Stability Results ◽  
Banach’S Contraction Principle

<abstract><p>In this article, we investigate sufficient conditions for the existence, uniqueness and Ulam-Hyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order $ 1 &lt; \varrho\leq 2 $ subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.</p></abstract>

scholarly journals Stability, Existence and Uniqueness of Boundary Value Problems for a Coupled System of Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 354 ◽  
Author(s):  
Mahmudov ◽  
Al-Khateeb
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Current Article ◽  
Fractional Differential ◽  
The Stability

The current article studies a coupled system of fractional differential equations with boundary conditions and proves the existence and uniqueness of solutions by applying Leray-Schauder’s alternative and contraction mapping principle. Furthermore, the Hyers-Ulam stability of solutions is discussed and sufficient conditions for the stability are developed. Obtained results are supported by examples and illustrated in the last section.

scholarly journals Analysis of Coupled System of Implicit Fractional Differential Equations Involving Katugampola–Caputo Fractional Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Manzoor Ahmad ◽  
Jiqiang Jiang ◽  
Akbar Zada ◽  
Syed Omar Shah ◽  
Jiafa Xu
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

In this paper, we study the existence and uniqueness of solutions to implicit the coupled fractional differential system with the Katugampola–Caputo fractional derivative. Different fixed-point theorems are used to acquire the required results. Moreover, we derive some sufficient conditions to guarantee that the solutions to our considered system are Hyers–Ulam stable. We also provided an example that explains our results.

A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions

2019 ◽  
Vol 22 (3) ◽  
pp. 601-618 ◽  
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouya
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Significant Contribution ◽  
Uniqueness Of Solutions ◽  
Coupled Boundary Conditions ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

Abstract This paper studies the existence and uniqueness of solutions for a new boundary value problem of coupled nonlinear multi-term fractional differential equations supplemented with three-point coupled boundary conditions. We make use of Banach’s contraction principle and Leray-Schauder’s alternative to derive the desired results, which are well illustrated with examples. We emphasize that the obtained results are new and make a significant contribution to the existing literature on the topic.

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.

STABILITY OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN THE FRAME OF ATANGANA-BALEANU OPERATOR

2021 ◽  
Vol 10 (5) ◽  
pp. 2319-2333
Author(s):  
A. George Maria Selvam ◽  
S. Britto Jacob
Keyword(s):  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Qualitative Properties ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Banach Contraction ◽  
Different Types ◽  
Singular Kernels ◽  
Fractional Differential ◽  
The Stability

Theory of fractional calculus with singular and non-singular kernels is pioneering and has garnered significant interest recently. Fair amount of literature on the qualitative properties of fractional differential and integral equations involving different types of operators is available. This manuscript aims to analyze the stability of a class of nonlinear fractional differential equation in terms of Atangana-Baleanu-Caputo operator. Sufficient conditions for the existence and uniqueness of solutions are obtained by employing classical fixed point theorems and Banach contraction principle. Also adequate conditions for Hyers-Ulam stability are established. To substantiate our analytic results, an example is provided with numerical simulation.

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 Ulam–Hyers Stability and Uniqueness for Nonlinear Sequential Fractional Differential Equations Involving Integral Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 235
Author(s):  
Areen Al-khateeb ◽  
Hamzeh Zureigat ◽  
Osama Ala’yed ◽  
Sameer Bawaneh
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Governing System ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equation ◽  
Banach’S Contraction Principle ◽  
Sequential Fractional Differential Equations

Fractional-order boundary value problems are used to model certain phenomena in chemistry, physics, biology, and engineering. However, some of these models do not meet the existence and uniqueness required in the mainstream of mathematical processes. Therefore, in this paper, the existence, stability, and uniqueness for the solution of the coupled system of the Caputo-type sequential fractional differential equation, involving integral boundary conditions, was discussed, and investigated. Leray–Schauder’s alternative was applied to derive the existence of the solution, while Banach’s contraction principle was used to examine the uniqueness of the solution. Moreover, Ulam–Hyers stability of the presented system was investigated. It was found that the theoretical-related aspects (existence, uniqueness, and stability) that were examined for the governing system were satisfactory. Finally, an example was given to illustrate and examine certain related aspects.

scholarly journals Stability analysis for first-order nonlinear differential equations with three-point boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
pp. 40-52
Author(s):  
Kamala E. Ismayilova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Fixed Point Principle ◽  
The Stability ◽  
The Given ◽  
Stability Results

AbstractIn the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. The uniqueness theorem is proved by Banach fixed point principle, and the existence theorem is based on Schafer’s theorem. Then, we describe different types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability. We discuss the stability results providing suitable example.

scholarly journals Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huina Zhang ◽  
Wenjie Gao
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Fractional Differential

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of orderα,β∈(4,5]with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential

AbstractThis paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

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