Existence and uniqueness of solutions for a coupled system of sequential fractional differential equations with initial conditions

2020 ◽  
Vol 11 (4) ◽  
pp. 1731-1741 ◽  
Author(s):  
Hamid Baghani ◽  
Jehad Alzabut ◽  
Javad Farokhi-Ostad ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

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 Separated Boundary Value Problems of Sequential Caputo and Hadamard Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jessada Tariboon ◽  
Asawathep Cuntavepanit ◽  
Sotiris K. Ntouyas ◽  
Woraphak Nithiarayaphaks
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, we discuss the existence and uniqueness of solutions for new classes of separated boundary value problems of Caputo-Hadamard and Hadamard-Caputo sequential fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples.

scholarly journals Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ -Hilfer Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Phollakrit Wongsantisuk ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Coupled System ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
New Class ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving ψ -Hilfer fractional derivatives, supplemented with multipoint boundary conditions. We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. Examples illustrating the main results are also constructed.

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.

scholarly journals Fractional Singular Differential Systems of Lane–Emden Type: Existence and Uniqueness of Solutions

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 95
Author(s):  
Yazid Gouari ◽  
Zoubir Dahmani ◽  
Shan E. Farooq ◽  
Farooq Ahmad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Differential Systems ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential

A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details.

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.

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