scholarly journals On a coupled system of higher order nonlinear Caputo fractional differential equations with coupled Riemann–Stieltjes type integro-multipoint boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Ymnah Alruwaily ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Multipoint Boundary ◽  
Uniqueness Results ◽  
Caputo Fractional Differential Equations ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Stieltjes Type

AbstractWe study a coupled system of Caputo fractional differential equations with coupled non-conjugate Riemann–Stieltjes type integro-multipoint boundary conditions. Existence and uniqueness results for the given boundary value problem are obtained by applying the Leray–Schauder nonlinear alternative, the Krasnoselskii fixed point theorem and Banach’s contraction mapping principle. Examples are constructed to illustrate the obtained results.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

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.

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 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 Generalized Liouville–Caputo Fractional Differential Equations and Inclusions with Nonlocal Generalized Fractional Integral and Multipoint Boundary Conditions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 667 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Madeaha Alghanmi ◽  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integral Boundary ◽  
Multipoint Boundary ◽  
Generalized Fractional Integral ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

We develop the existence criteria for solutions of Liouville–Caputo-type generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral and multipoint boundary conditions. Modern techniques of functional analysis are employed to derive the main results. Examples illustrating the main results are also presented. It is imperative to mention that our results correspond to the ones for a symmetric second-order nonlocal multipoint integral boundary value problem under suitable conditions (see the last section).

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