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Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

  • Fatma Al-Musalhi EMAIL logo , Nasser Al-Salti and Erkinjon Karimov
Published/Copyright: March 13, 2018
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 21 Issue 1

Abstract

Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

MSC 2010: Primary 26A33; Secondary 34A08; 35R30; 33E12; 35R11; 35C10
Key Words and Phrases: initial boundary value problems; inverse problems; fractional differential equations; hyper-Bessel operators; Erdélyi-Kober fractional order operators; series solutions; Mittag-Leffler functions

Acknowledgements

Authors would like to thank Prof. V. Kiryakova for her valuable comments and suggestions. Authors also acknowledge financial support from the Research Council (TRC), Oman. This work is funded by TRC under the research agreement No. ORG/SQU/CBS/13/030.

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Received: 2017-10-25
Published Online: 2018-3-13
Published in Print: 2018-2-23

© 2018 Diogenes Co., Sofia

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  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
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  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
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https://doi.org/10.1515/fca-2018-0013
Keywords for this article
initial boundary value problems; inverse problems; fractional differential equations; hyper-Bessel operators; Erdélyi-Kober fractional order operators; series solutions; Mittag-Leffler functions

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
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