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Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications
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Mohammed Al-Refai
Veröffentlicht/Copyright:
28. August 2015
Abstract
In this paper, we formulate and prove the weak and strong maximum principles for a general parabolic-type fractional differential operator with the Riemann–Liouville time-fractional derivative of distributed order. The proofs of the maximum principles are based on an estimate of the Riemann–Liouville fractional derivative at its maximum point that was recently derived by the authors. Some a priori norm estimates for solutions to initial-boundary value problems for linear and nonlinear fractional diffusion equations of distributed order and uniqueness results for these problems are presented.
Keywords: Riemann–Liouville fractional derivative; distributed-order time-fractional diffusion equation; initial-boundary value problems; maximum principle; uniqueness theorem; stability; linear equation of distributed order; nonlinear equation of distributed order
Received: 2015-6-24
Accepted: 2015-7-26
Published Online: 2015-8-28
Published in Print: 2016-5-1
© 2016 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Weighted mixed spherical means and singular ultrahyperbolic equation
- Fractional approximation of solutions of evolution equations
- Forecasting of random sequences and Prony decomposition of finance data
- On Volterra functions and Ramanujan integrals
- An inverse problem for a multidimensional fractional diffusion equation
- Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications
Artikel in diesem Heft
- Frontmatter
- Weighted mixed spherical means and singular ultrahyperbolic equation
- Fractional approximation of solutions of evolution equations
- Forecasting of random sequences and Prony decomposition of finance data
- On Volterra functions and Ramanujan integrals
- An inverse problem for a multidimensional fractional diffusion equation
- Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications
