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

  • Rizwan Rizwan EMAIL logo , Akbar Zada ORCID logo , Hira Waheed and Usman Riaz
Published/Copyright: August 25, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 6

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.

Keywords: Hilfer fractional derivative; Langevin equation; instantaneous impulses; Ulam–Hyers–Rassias stability
MSC 2010: 26A33; 34A08; 34B27
Corresponding author: Rizwan Rizwan, Department of Mathematics, University of Buner, Buner, Pakistan, E-mail:

  1. Author contribution: All the authors contributed equally and significantly in writing this paper. All the authors read and approved the final manuscript.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare that they have no competing interests regarding this research work.

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Received: 2020-10-22
Revised: 2021-03-15
Accepted: 2021-07-20
Published Online: 2021-08-25

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
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https://doi.org/10.1515/ijnsns-2020-0240
Keywords for this article
Hilfer fractional derivative; Langevin equation; instantaneous impulses; Ulam–Hyers–Rassias stability

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
  9. Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
  10. Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
  11. Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
  12. Two occurrences of fractional actions in nonlinear dynamics
  13. Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
  14. Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
  15. Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
  16. Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
  17. Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
  18. Pandemic management by a spatio–temporal mathematical model
  19. Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
  20. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
  21. Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
  22. Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
  23. Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
  24. Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
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