In this paper, we study the fractional p -Laplacian evolution equation with arbitrary initial energy, u t ( x , t ) + ( Δ ) p s u ( x , t ) = f ( u ( x , t ) ) , x ∈Ω , t > 0 , $$\\begin{array}{} \\displaystyle u_t(x,t) + (-{\\it\\Delta})_p^s...
P Aceves-Sanchez,L Cesbron 摘要: This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov- Fokker-Planck equation in which the Laplacian is replaced by a fractional Laplacian. The evolution of the density is governed by a fractional heat equation with the addition...
ON THE CAUCHY-PROBLEM AND INITIAL TRACES FOR THE EVOLUTION P-LAPLACIAN EQUATIONS WITH STRONGLY NONLINEAR SOURCES Not Available JN Zhao - 《Journal of Differential Equations》 被引量: 149发表: 1995年 Series Expansions for the First Passage Distribution of Wong-Pearson Jump-Diffusions We explore the ...
Δ represents the usual Laplacian operator. In the actual world, and during an epidemic, there are numerous components that varies and can influence the outbreak of a disease and cannot be included in the model formulation, as the fear generated by the population from infection, weather (...
We study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy ...
S.— ROSS, B.: An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. Search in Google Scholar [19] MOPHOU, G. M.— N’GUÉRÉKATA, G. M.: Existence of mild solutions of some semilinear neutral fractional functional evolution equations with ...
Multiple positive solutions of four-point nonlinear boundary value problems for higher-order p-Laplacian operator with all derivatives Nonlinear Anal.: Theory Method Appl., 71 (9) (2009), pp. 4309-4319 View PDFView articleView in ScopusGoogle Scholar [4] V Caselles, R Kimmel, G Sapiro Geodes...
where p . v . p.v. denotes for the Cauchy principle value, | x − y | |𝑥−𝑦| is the Euclidean distance between x 𝑥 and y 𝑦, and Γ ( · ) Γ(·) is the Gamma function. The fractional Laplacian in R d ℝ𝑑 can also be defined as the pseudo-differential ope...
Geometrical Structure of Laplacian Eigenfunctions. SIAM Rev. 2013, 55, 601–667. [Google Scholar] [CrossRef] [Green Version] Meerschaert, M.M.; Nane, E.; Vellaisamy, P. Fractional Cauchy problems on bounded domains. Ann. Probab. 2009, 37, 979–1007. [Google Scholar] [CrossRef] Nane,...
[18]. A fractional Laplacian has been introduced into the Schrödinger equation by some researchers [14], [15]. While the impact and usefulness of such quantum theory remains questionable, some of the ideas and methods have gone beyond their original framework, with potential application to ...