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.

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 Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 341 ◽  
Author(s):  
Zeeshan Ali ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Akbar Zada
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
Existence Theory ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Classical Technique ◽  
Fractional Differential ◽  
Stability Results

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

scholarly journals Nonlinear functional analysis

1983 ◽  
Vol 2 (3) ◽  
pp. 162-165
Author(s):  
W. L. Fouché
Keyword(s):  
Functional Analysis ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Homotopy Theory ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Infinite Dimensional ◽  
Contraction Theorem ◽  
New Ideas

In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.

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