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Functional delay fractional equations

  • Tadeusz Jankowski
Published/Copyright: August 27, 2016
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 19 Issue 4

Abstract

In this paper we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by using the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.

Key Words and Phrases: delay fractional equations; Banach fixed point theorem; method of successive approximations; existence of solutions
MSC 2010: 34K37; 34K40

References

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Received: 2015-4-3
Published Online: 2016-8-27
Published in Print: 2016-8-1

© 2016 Diogenes Co., Sofia

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
https://doi.org/10.1515/fca-2016-0057
Keywords for this article
delay fractional equations; Banach fixed point theorem; method of successive approximations; existence of solutions

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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