A coupled system of nonlinear Caputo–Hadamard Langevin equations associated with nonperiodic boundary conditions

2020 ◽  
Vol 44 (3) ◽  
pp. 2650-2670
Author(s):  
Mohammed M. Matar ◽  
Jehad Alzabut ◽  
Jagan Mohan Jonnalagadda
Keyword(s):  
Boundary Conditions ◽  
Coupled System ◽  
Langevin Equations

scholarly journals Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Zaid Laadjal ◽  
Qasem M. Al-Mdallal ◽  
Fahd Jarad
Keyword(s):  
Boundary Conditions ◽  
Coupled System ◽  
Fractional Integrals ◽  
Langevin Equations ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Nonseparated Boundary Conditions ◽  
New Type ◽  
Predictor Corrector ◽  
Derivatives Of

In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss–Seidel method in order to solve some specific particular cases of the system.

scholarly journals Existence of Solution for a Fractional Langevin System with Nonseparated Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Of Solution ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Type Integral

In this paper, we investigate the existence and uniqueness of a coupled system of nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. We use Banach’s and Krasnoselskii’s fixed point theorems to obtain the results. Lastly, we give two examples to show the effectiveness of the main results.

scholarly journals Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Ahmed Salem ◽  
Faris Alzahrani ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Research Paper ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

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