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Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function

  • Mohammed Al-Refai
Published/Copyright: August 23, 2021
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 24 Issue 4

Abstract

In this paper, we formulate and prove two maximum principles to nonlinear fractional differential equations. We consider a fractional derivative operator with Mittag-Leffler function of two parameters in the kernel. These maximum principles are used to establish a pre-norm estimate of solutions, and to derive certain uniqueness and positivity results to related linear and nonlinear fractional initial value problems.

MSC 2010: Primary 26A33; Secondary 34K37; 35B50
Key Words and Phrases: fractional order derivative; fractional differential equations; maximum principle; Mittag-Leffler function

References

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Received: 2020-09-27
Revised: 2021-07-13
Published Online: 2021-08-23
Published in Print: 2021-08-26

© 2021 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 24–4–2021)
  4. Research Paper
  5. Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
  6. Tutorial paper
  7. The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
  8. Research Paper
  9. Fractional diffusion-wave equations: Hidden regularity for weak solutions
  10. Censored stable subordinators and fractional derivatives
  11. Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
  12. Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
  13. Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
  14. The rate of convergence on fractional power dissipative operator on compact manifolds
  15. Fractional Langevin type equations for white noise distributions
  16. Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
  17. Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
  18. The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
  19. Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
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https://doi.org/10.1515/fca-2021-0052
Keywords for this article
fractional order derivative; fractional differential equations; maximum principle; Mittag-Leffler function

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 24–4–2021)
  4. Research Paper
  5. Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
  6. Tutorial paper
  7. The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
  8. Research Paper
  9. Fractional diffusion-wave equations: Hidden regularity for weak solutions
  10. Censored stable subordinators and fractional derivatives
  11. Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
  12. Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
  13. Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
  14. The rate of convergence on fractional power dissipative operator on compact manifolds
  15. Fractional Langevin type equations for white noise distributions
  16. Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
  17. Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
  18. The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
  19. Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
  20. Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems
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