On Maximal Regularity for Abstract Parabolic Problems with Fractional Time Derivative
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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… read more here.
Keywords: time derivative; regularity abstract; regularity; maximal regularity ... See more keywords
Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel
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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,… read more here.
Keywords: equation fractional; fractional time; nonsingular mittag; time derivative ... See more keywords
Stability and convergence analysis of a semi-implicit fractional FEM-scheme for non-Newtonian fluid flows of polymer aqueous solutions with fractional time-derivative
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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… read more here.
Keywords: scheme; fractional time; non newtonian; semi implicit ... See more keywords
First passage times for some classes of fractional time-changed diffusions
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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… read more here.
Keywords: time changed; time; fractional time; first passage ... See more keywords
Global Unsolvability of the Burgers Equation with Fractional Time Derivative
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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. read more here.
Keywords: time; burgers equation; equation fractional; unsolvability burgers ... See more keywords
A Fractional-in-Time Prey-Predator Model with Hunting Cooperation: Qualitative Analysis, Stability and Numerical Approximations
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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… read more here.
Keywords: prey predator; hunting cooperation; model; fractional time ... See more keywords