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Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

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Published/Copyright: May 9, 2020
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 23 Issue 2

Abstract

Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

MSC 2010: Primary 35J67; Secondary 45P05
Key Words and Phrases: fractional Laplacian; boundary conditions; boundary integral equations

Acknowledgements

The project has been supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00001). This work was completed in the ELTE Institutional Excellence Program (1783-3/2018/FEKUTSRAT) supported by the Hungarian Ministry of Human Capacities.

References

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Received: 2019-04-25
Published Online: 2020-05-09
Published in Print: 2020-04-28

© 2020 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–2–2020)
  4. Survey Paper
  5. Porous functions – II
  6. Research Paper
  7. On a non–local problem for a multi–term fractional diffusion-wave equation
  8. A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique
  9. Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions
  10. Global existence and large time behavior of solutions of a time fractional reaction diffusion system
  11. Evaluation of fractional order of the discrete integrator. Part II
  12. Subordination principle for fractional diffusion-wave equations of Sobolev type
  13. Time-changed fractional Ornstein-Uhlenbeck process
  14. Fractional problems with critical nonlinearities by a sublinear perturbation
  15. New finite-time stability analysis of singular fractional differential equations with time-varying delay
  16. Reflection properties of zeta related functions in terms of fractional derivatives
  17. α-fractionally convex functions
  18. On the kinetics of Hadamard-type fractional differential systems
  19. Asymptotic stability of fractional difference equations with bounded time delays
  20. Short Paper
  21. The continuation of solutions to systems of Caputo fractional order differential equations
  22. Erratum
  23. Erratum: On modifications of the exponential integral with the Mittag-Leffler function
https://doi.org/10.1515/fca-2020-0018
Keywords for this article
fractional Laplacian; boundary conditions; boundary integral equations

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–2–2020)
  4. Survey Paper
  5. Porous functions – II
  6. Research Paper
  7. On a non–local problem for a multi–term fractional diffusion-wave equation
  8. A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique
  9. Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions
  10. Global existence and large time behavior of solutions of a time fractional reaction diffusion system
  11. Evaluation of fractional order of the discrete integrator. Part II
  12. Subordination principle for fractional diffusion-wave equations of Sobolev type
  13. Time-changed fractional Ornstein-Uhlenbeck process
  14. Fractional problems with critical nonlinearities by a sublinear perturbation
  15. New finite-time stability analysis of singular fractional differential equations with time-varying delay
  16. Reflection properties of zeta related functions in terms of fractional derivatives
  17. α-fractionally convex functions
  18. On the kinetics of Hadamard-type fractional differential systems
  19. Asymptotic stability of fractional difference equations with bounded time delays
  20. Short Paper
  21. The continuation of solutions to systems of Caputo fractional order differential equations
  22. Erratum
  23. Erratum: On modifications of the exponential integral with the Mittag-Leffler function
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