On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative
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DOI: 10.1002/mma.6103
Abstract: In this paper, we study a backward problem for a fractional diffusion equation with nonlinear source in a bounded domain. By applying the properties of Mittag‐Leffler functions and Banach fixed point theorem, we establish some… read more here.
Keywords: problem fractional; diffusion equation; problem; final value ... See more keywords
The Brezis–Nirenberg problem for fractional systems with Hardy potentials
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DOI: 10.1002/mma.7856
Abstract: In this work, we study the existence of positive solutions to the following fractional elliptic systems with Hardy‐type singular potentials and coupled by critical homogeneous nonlinearities (−Δ)su−μ1u|x|2s=|u|2s∗−2u+ηα2s∗|u|α−2|v|βu+12Qu(u,v)inΩ,(−Δ)sv−μ2v|x|2s=|v|2s∗−2v+ηβ2s∗|u|α|v|β−2v+12Qv(u,v)inΩ,u,v>0inΩ,u=v=0inℝN\Ω, where (− Δ)s denotes the fractional Laplace operator, Ω⊂ℝN… read more here.
Keywords: brezis nirenberg; systems hardy; problem fractional; fractional systems ... See more keywords
The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
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DOI: 10.1007/s00013-021-01594-0
Abstract: We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of… read more here.
Keywords: spaces partial; fractional sobolev; condition; problem fractional ... See more keywords
Principal eigenvalue of mixed problem for the fractional Laplacian: Moving the boundary conditions
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DOI: 10.1016/j.jde.2018.03.001
Abstract: Abstract We analyze the behavior of the eigenvalues of the following nonlocal mixed problem { ( − Δ ) s u = λ 1 ( D ) u in Ω , u = 0 in … read more here.
Keywords: eigenvalue mixed; fractional laplacian; problem fractional; mixed problem ... See more keywords
On the initial value problem for fractional Volterra integrodifferential equations with a Caputo–Fabrizio derivative
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Modelling of Natural Phenomena"
DOI: 10.1051/mmnp/2021010
Abstract: In this paper, a time-fractional integrodifferential equation with the Caputo–Fabrizio type derivative will be considered. The Banach fixed point theorem is the main tool used to extend the results of a recent paper of Tuan… read more here.
Keywords: time; value problem; initial value; fractional volterra ... See more keywords
The Cauchy Problem for the Fractional Diffusion Equation in a Weighted Hölder Space
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DOI: 10.1134/s0037446618060071
Abstract: Under study is the Cauchy problem for the fractional diffusion equation with a Caputo derivative. The existence and uniqueness theorems for a smooth solution are proven in a weighted H¨older space. read more here.
Keywords: fractional diffusion; diffusion equation; cauchy problem; problem fractional ... See more keywords
Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations
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DOI: 10.3390/sym10090358
Abstract: In this work, a three-point boundary value problem of fractional q-difference equations is discussed. By using fixed point theorems on mixed monotone operators, some sufficient conditions that guarantee the existence and uniqueness of positive solutions… read more here.
Keywords: three point; value problem; problem fractional; point ... See more keywords
Positive Solutions for a Class of Integral Boundary Value Problem of Fractional q-Difference Equations
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DOI: 10.3390/sym14112465
Abstract: This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new… read more here.
Keywords: problem fractional; integral boundary; class integral; fractional difference ... See more keywords