Results 71 to 80 of about 2,952,428 (298)
Axioms, 2014 This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann ...
Ram K. Saxena +2 more
doaj +1 more source
Fractional diffusion equation and diffusive stresses [PDF]
PAMM, 2007 AbstractA quasi‐static uncoupled theory of diffusive stresses based on the time‐fractional diffusion equation is considered. The Caputo fractional derivative of order α is used. In particular, the proposed theory interpolates the classical theory of diffusive stresses and that without energy dissipation.
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Numerical methods for solving the multi-term time-fractional wave-diffusion equation [PDF]
, 2013 In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4 ...
Pinghui Zhuang +13 more
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Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Neurochemical levels measured by brain MR spectroscopy (MRS) have been proposed as endpoints for clinical trials in early‐stage spinocerebellar ataxia (SCA) trials. We tested their trial‐readiness by quantifying neurochemicals in three affected brain regions in early‐stage cohorts of SCA2 and SCA3, examining their reproducibility in ...
James M. Joers +19 more
wiley +1 more source
Inverse problem for fractional diffusion equation [PDF]
Fractional Calculus and Applied Analysis, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multidimensional Time Fractional Diffusion Equation [PDF]
, 2017 In this paper we present integral and series representations for the fundamental solution of the time fractional diffusion equation in an arbitrary dimension. The series representation obtained depends on the parity of the dimension. As an application of our results we study the diffusion and stress in the axially symmetric case for plane deformation ...
Ferreira, Milton dos Santos +1 more
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Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation [PDF]
, 2005 The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order in (0,1).
Anh, Vo +7 more
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Optimal Control of a Fractional Diffusion Equation with Delay [PDF]
, 2014 We study a homogeneous Dirichlet boundary fractional diffusion equation with delay in a bounded domain. The fractional time derivative is considered in the left Caputo sense. By means of a linear continuous operator, we first transform the
Mophou, Gisèle +3 more
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T1 Over Squared Proton Density Ratio to Characterize Multiple Sclerosis Lesions
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Differentiating remyelinated from demyelinated lesions in MS remains challenging without histological confirmation. This study introduces the T1‐to‐PD2 ratio (TPR) imaging approach and evaluates its ability to characterize MS lesions alongside other quantitative MRI (qMRI) metrics. Methods Thirty individuals with MS (mean age: 47.5 ±
Sarah J. Wright +10 more
wiley +1 more source
Finite element method for space-time fractional diffusion equation [PDF]
, 2016 In this paper, we consider two types of space-time fractional diffusion equations(STFDE) on a finite domain. The equation can be obtained from the standard diffusion equation by replacing the second order space derivative by a Riemann-Liouville ...
Turner, Ian +4 more
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