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Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1309-y
Abstract: We consider initial value problems for abstract evolution equations with fractional time derivative. Concerning the Caputo derivative $$\mathbb {D}^\alpha u$$Dαu, we show that certain assumptions, which are known to be sufficient to get a unique…
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Keywords:
time derivative;
regularity abstract;
regularity;
maximal regularity ... See more keywords
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Published in 2019 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-018-1305-6
Abstract: In this paper, we consider a diffusion equation with fractional time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. We first prove the existence and uniqueness of solution by means of a spectral argument. Then,…
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Keywords:
equation fractional;
fractional time;
nonsingular mittag;
time derivative ... See more keywords
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Published in 2020 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-020-1110-3
Abstract: In this paper, a fully discrete fractional semi-implicit FEM-scheme is developed to study the non-Newtonian fluid flow of polymer aqueous solutions in a two-dimensional domain using Caputo’s fractional time-derivative. The fractional-time scheme is coupled with…
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Keywords:
scheme;
fractional time;
non newtonian;
semi implicit ... See more keywords
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Published in 2021 at "Stochastic Analysis and Applications"
DOI: 10.1080/07362994.2021.1953386
Abstract: We consider some time-changed diffusion processes obtained by applying the Doob transformation rule to a time-changed Brownian motion. The time-change is obtained via the inverse of an α-stable subordinator. These processes are specified in terms…
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Keywords:
time changed;
time;
fractional time;
first passage ... See more keywords
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Published in 2019 at "Differential Equations"
DOI: 10.1134/s0012266119060156
Abstract: We obtain sufficient conditions for the nonexistence of time-global solutions of a fractional analog of the Burgers equation. Examples of solution blowup are considered for the Cauchy problem. The Mitidieri-Pokhozhaev nonlinear capacity method is used.
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Keywords:
time;
burgers equation;
equation fractional;
unsolvability burgers ... See more keywords
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Published in 2021 at "Axioms"
DOI: 10.3390/axioms10020078
Abstract: A prey–predator system with logistic growth of prey and hunting cooperation of predators is studied. The introduction of fractional time derivatives and the related persistent memory strongly characterize the model behavior, as many dynamical systems…
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Keywords:
prey predator;
hunting cooperation;
model;
fractional time ... See more keywords