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1
Content available remote Ground-state representation for the fractional Laplacian on the half-line
Jakubowski Tomasz, Maciocha Paweł
Probability and Mathematical Statistics
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2023
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Vol. 43, Fasc. 1
83--108
EN
We give a ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line
2
Content available remote Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
Bidi Younes, Beniani Abderrahmane, Zennir Khaled, Himadan Ahmed
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
245--258
EN
We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.
3
Content available A unique weak solution for a kind of coupled system of fractional Schrodinger equations
Abdolrazaghi Fatemeh, Razani Abdolrahman
Opuscula Mathematica
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2020
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Vol. 40, no. 3
313--322
EN
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrodinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
4
Content available remote Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion
Villa-Morales José
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
269--276
EN
In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.
5
Content available remote On the Distribution and q-Variation of the Solution to the Heat Equation with Fractional Laplacian
Khalil Z. Mahdi, Tudor C. A.
Probability and Mathematical Statistics
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2019
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Vol. 39, Fasc. 2
315--335
EN
We study the probability distribution of the solution to the linear stochastic heat equation with fractional Laplacian and white noise in time and white or correlated noise in space. As an application, we deduce the behavior of the q-variations of the solution in time and in space.
6
Content available On fractional vectorial calculus
Ortigueira M. D., Machado J. T. M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
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Vol. 66, nr 4
389--402
EN
This paper reviews the fractional vectorial differential operators proposed previously and introduces the fractional versions of the classic Green’s, Stokes’, and Ostrogradski-Gauss’s integral theorems. The suitability of fractional derivatives for sciences and the Laplacian definition are also discussed.
7
Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators
Yangari M.
Journal of Applied Analysis
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2016
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Vol. 22, nr 1
55--65
EN
The aim of this paper is to study the large-time behaviour of mild solutions to the one-dimensional cooperative systems with anomalous diffusion when at least one entry of the initial condition decays slower than a power. We prove that the solution moves at least exponentially fast as time goes to infinity. Moreover, the exponent of propagation depends on the decay of the initial condition and of the reaction term.
8
Content available remote On the Existence of a Non-trivial Non-negative Global Radial Weak Solution to a Fractional Laplacian Problem with a Singular Potential
Bayrami M., Hesaaraki M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2016
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Vol. 64, no. 2/3
175--183
EN
We prove the existence of a non-trivial non-negative radial weak solution to the problem [wzór]. Here N > 2α, α ∈ (1/2,1), 1 < r < p < [wzór] and μ ∈ R. We also assume that b > 0 and 0 < λ < [wzór].
9
Content available remote Gradient perturbations of the sum of two fractional laplacians
Szczypkowski K.
Probability and Mathematical Statistics
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2012
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Vol. 32, Fasc. 1
41--46
EN
We study the gradient perturbations of Δα/2 + Δβ/2 with 0 < β <<α<<2 and α > 1.
10
Content available remote On the Schroedinger operator based on the fractional Laplacian
Bogdan K., Byczkowski T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2001
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Vol. 49, no 3
291-301
EN
We announce new results in the potential theory of Schroedinger operators based on the fractional Laplacian on Euclidean spaces of arbitrary dimension. We concentrate on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of symmetric [alpha]-stable Levy processes on Rd, including the recurrent case. We also provide some explicit examples of gauge functions for a general class of domains.
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