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The Neumann problem for the generalized Bagley-Torvik fractional differential equation

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Published/Copyright: August 28, 2016
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 19 Issue 4

Abstract

We discuss the existence and multiplicity of solutions to the generalized Bagley-Torvik fractional differential equation u″ = AcDαu + f (t, u, u′) satisfying the Neumann boundary conditions u′ (0) = u′ (T ) = 0. The solvability of the problem is proved by the combination of the Leray-Schauder degree method with the extremal principle.

MSC 2010: Primary 26A33; 34A08; Secondary 34B15; 33E12
Key Words and Phrases: Bagley-Torvik fractional differential equation; Neumann problem; extremal principle; Caputo fractional derivative; existence; multiplicity

Acknowledgements

Supported by the grant No. 14-06958S of the Grant Agency of the Czech Republic.

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Received: 2015-10-2
Published Online: 2016-8-28
Published in Print: 2016-8-1

© 2016 Diogenes Co., Sofia

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https://doi.org/10.1515/fca-2016-0049
Keywords for this article
Bagley-Torvik fractional differential equation; Neumann problem; extremal principle; Caputo fractional derivative; existence; multiplicity

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA Related News, Events and Books (FCAA–Volume 19–4–2016)
  4. Survey Paper
  5. Responses comparison of the two discrete-time linear fractional state-space models
  6. Survey Paper
  7. A survey on impulsive fractional differential equations
  8. Research Paper
  9. Generalization of the fractional poisson distribution
  10. Research Paper
  11. Diffusivity identification in a nonlinear time-fractional diffusion equation
  12. Research Paper
  13. An extension problem for the fractional derivative defined by Marchaud
  14. Research Paper
  15. Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
  16. Research Paper
  17. The Neumann problem for the generalized Bagley-Torvik fractional differential equation
  18. Research Paper
  19. On the fractional probabilistic Taylor's and mean value theorems
  20. Research Paper
  21. Time-fractional heat conduction in a two-layer composite slab
  22. Research Paper
  23. Weighted adams type theorem for the riesz fractional integral in generalized morrey space
  24. Research Paper
  25. Fractional schrödinger equation with zero and linear potentials
  26. Research Paper
  27. Positive solutions of higher-order nonlinear multi-point fractional equations with integral boundary conditions
  28. Research Paper
  29. Weighted bounded solutions for a class of nonlinear fractional equations
  30. Research Paper
  31. Existence and global asymptotic behavior of positive solutions for superlinear fractional dirichlet problems on the half-line
  32. Short Paper
  33. Functional delay fractional equations
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