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On solutions of linear fractional differential equations and systems thereof

  • Khongorzul Dorjgotov EMAIL logo , Hiroyuki Ochiai and Uuganbayar Zunderiya
Published/Copyright: May 11, 2019
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 22 Issue 2

Abstract

We derive exact solutions to classes of linear fractional differential equations and systems thereof expressed in terms of generalized Wright functions and Fox H-functions. These solutions are invariant solutions of diffusion-wave equations obtained through certain transformations, which are briefly discussed. We show that the solutions given in this work contain previously known results as particular cases.

MSC 2010: Primary: 34A08; 26A33; Secondary: 35R11; 34A05
Key Words and Phrases: fractional differential equations; exact solutions; generalized Wright function; Fox H-function

Acknowledgements

We are very grateful to the editors whose valuable suggestions and comments helped us to improve the content of the manuscript. This work was supported by JSPS (KAKENHI Grant No. 15H03613) and by the Foundation of Science and Technology of Mongolia (Grant No. SSA-012/2016).

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Received: 2017-10-02
Revised: 2019-02-07
Published Online: 2019-05-11
Published in Print: 2019-04-24

© 2019 Diogenes Co., Sofia

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  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 22–2–2019)
  4. Discussion Paper
  5. The flaw in the conformable calculus: It is conformable because it is not fractional
  6. The failure of certain fractional calculus operators in two physical models
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  9. On Riesz derivative
  10. A note on fractional powers of strongly positive operators and their applications
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  21. On representation and interpretation of Fractional calculus and fractional order systems
https://doi.org/10.1515/fca-2019-0028
Keywords for this article
fractional differential equations; exact solutions; generalized Wright function; Fox H-function

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 22–2–2019)
  4. Discussion Paper
  5. The flaw in the conformable calculus: It is conformable because it is not fractional
  6. The failure of certain fractional calculus operators in two physical models
  7. Research Paper
  8. Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
  9. On Riesz derivative
  10. A note on fractional powers of strongly positive operators and their applications
  11. Semi-fractional diffusion equations
  12. Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
  13. Well-posedness of fractional degenerate differential equations in Banach spaces
  14. Structure factors for generalized grey Browinian motion
  15. Linear stationary fractional differential equations
  16. Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
  17. On fractional differential inclusions with Nonlocal boundary conditions
  18. On solutions of linear fractional differential equations and systems thereof
  19. Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
  20. A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
  21. On representation and interpretation of Fractional calculus and fractional order systems
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