scholarly journals Switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives

2020 ◽  
Author(s):  
Rizwan Rizwan ◽  
Akbar Zada ◽  
Syed Omar Shah
Keyword(s):  
Coupled System ◽  
Langevin Equations ◽  
Mixed Derivatives

scholarly journals Switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives

2021 ◽  
Vol 6 (12) ◽  
pp. 13092-13118
Author(s):  
Rizwan Rizwan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
Akbar Zada ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Langevin Equations ◽  
Fixed Point Approach ◽  
Proposed Model ◽  
Mixed Derivatives ◽  
Rassias Stability

<abstract><p>In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.</p></abstract>

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 Nonlocal coupled system for $ \psi $-Hilfer fractional order Langevin equations

2021 ◽  
Vol 6 (9) ◽  
pp. 9731-9756
Author(s):  
Weerawat Sudsutad ◽  
◽  
Sotiris K. Ntouyas ◽  
Chatthai Thaiprayoon ◽  
◽  
...  
Keyword(s):  
Fractional Order ◽  
Coupled System ◽  
Langevin Equations

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.

Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Rizwan Rizwan ◽  
Akbar Zada ◽  
Hira Waheed ◽  
Usman Riaz
Keyword(s):  
Functional Analysis ◽  
Fixed Point ◽  
Fractional Order ◽  
Coupled System ◽  
Langevin Equations ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Proposed Model ◽  
Ulam’S Type Stability ◽  
Stability Results

Abstract In this manuscript, switched coupled system of nonlinear impulsive Langevin equations involving four Hilfer fractional-order derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss the existence, uniqueness, and Ulam’s type stability results of our proposed model, with the help of Schaefer’s fixed point theorem. An example is provided at the end to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document