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Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2

  • Chendrayan Dineshkumar , Velusamy Vijayakumar ORCID logo EMAIL logo , Ramalingam Udhayakumar ORCID logo , Anurag Shukla and Kottakkaran Sooppy Nisar
Published/Copyright: October 6, 2022
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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 5

Abstract

The main motivation of our conversation is the existence and approximate controllability for fractional stochastic Volterra–Fredholm integro-differential systems having order 1 < r < 2. The primary outcomes are obtained by applying concepts and ideas from fractional calculus, multivalued maps, the theory of cosine family, Martelli and Dhage, and Leray–Schauder fixed point techniques. We begin by emphasizing the existence, and then demonstrate the approximate controllability of the considered system. Additionally, we determine the approximate controllability outcomes for the system with infinite delay. At last, an application is established for drawing the theoretical conclusions of primary outcomes.

Keywords: approximate controllability; fractional derivative; infinite delay; nonlocal conditions; stochastic system; Volterra–Fredholm integro-differential system
2010 Subject Classification: 26A33; 34A08; 34K30; 47D09; 45D05; 93E03
Corresponding author: Velusamy Vijayakumar, Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamilnadu, India, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: There are no funders to report for this submission.

  3. Conflict of interest statement: This work does not have any conflicts of interest.

  4. Data availability statement: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Received: 2021-12-29
Revised: 2022-07-24
Accepted: 2022-09-18
Published Online: 2022-10-06

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0479
Keywords for this article
approximate controllability; fractional derivative; infinite delay; nonlocal conditions; stochastic system; Volterra–Fredholm integro-differential system

Articles in the same Issue

  1. Frontmatter
  2. Original Research Article
  3. Hybrid solitary wave solutions of the Camassa–Holm equation
  4. Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
  5. A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
  6. Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
  7. Numerical modeling of the dam-break flood over natural rivers on movable beds
  8. A class of piecewise fractional functional differential equations with impulsive
  9. Lie symmetry analysis for two-phase flow with mass transfer
  10. Asymptotic behavior for stochastic plate equations with memory in unbounded domains
  11. Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
  12. A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
  13. Ground state solutions of Schrödinger system with fractional p-Laplacian
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  16. Hilfer fractional stochastic evolution equations on infinite interval
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  22. Shehu transform on time-fractional Schrödinger equations – an analytical approach
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  24. Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
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