Search for dissertations about: "fractional equation"

Showing result 1 - 5 of 17 swedish dissertations containing the words fractional equation.

2. 1. The Finite Element Method for Fractional Order Viscoelasticity and the Stochastic Wave Equation

   Author : Fardin Saedpanah; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; finite element method; continuous Galerkin method; linear viscoelasticity; fractional calculus; fractional order viscoelasticity; weakly singular kernel; stability; a priori error estimate; a posteriori error estimate; stochastic wave equation; additive noise; Wiener process; strong convergence.; linear viscoelasticity;

   Abstract : This thesis can be considered as two parts. In the first part a hyperbolic type integro-differential equation with weakly singular kernel is considered, which is a model for dynamic fractional order viscoelasticity. In the second part, the finite element approximation of the linear stochastic wave equation is studied. READ MORE

4. 2. Models and numerical procedures for fractional order viscoelasticity

   Author : Klas Adolfsson; Chalmers tekniska högskola; []
   Keywords : TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; sparse quadrature; a posteriori error estimate; a priori error estimate; viscoelasticity; adaptivity; fractional calculus; large deformations; integro-differential equation; internal variables;

   Abstract : .... READ MORE

5. 3. Selected Topics in Mathematical Modelling: Machine Learning and Tugs-of-War

   Author : Carmina Fjellström; Kaj Nyström; Andrea Pascucci; Uppsala universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Machine learning; Neural networks; LSTM; Financial forecasting; Time series analysis; Stochastic gradient descent; Diffusion map; Dimension reduction; Tug-of-war games; Fractional heat operator; Mean value property; Infinity fractional heat operators; Dynamic programming principle; p-Laplacian; Infinity Laplacian; Kolmogorov equation; Stochastic games; Viscosity solutions; Tillämpad matematik och statistik; Applied Mathematics and Statistics;

   Abstract : This thesis concerns selected topics in mathematical modelling, namely in machine learning and stochastic games called tugs-of-war. It consists of four scientific articles. The first and second are about machine learning topics, while the third and fourth articles are about tug-of-war games. READ MORE

6. 4. The Continuous Galerkin Method for Fractional Order Viscoelasticity

   Author : Fardin Saedpanah; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES;

   Abstract : We consider a fractional order integro-differential equation with a weakly singular convolution kernel. The equation with homogeneous Dirichlet boundary conditions is reformulated as an abstract Cauchy problem, and well-posedness is verified in the context of linear semigroup theory. READ MORE

7. 5. A Differentiable Approach to Stochastic Differential Equations : the Smoluchowski Limit Revisited

   Author : Haidar Al-Talibi; Astrid Hilbert; Yaozhong Hu; Linnéuniversitetet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; α-stable Lévy noise; Fractional Brownian motion; Girsanov theorem; Mean-field model; Nonlinear stochastic oscillator; Ornstein-Uhlenbeck process; Scaling limit; Second order Itô equation; Time change.; Matematik; Mathematics;

   Abstract : In this thesis we generalize results by Smoluchowski [43], Chandrasekhar[6], Kramers, and Nelson [30]. Their aim is to construct Brownian motion as a limit of stochastic processes with differentiable sample paths by exploiting a scaling limit which is a particular type of averaging studied by Papanicolao [35]. READ MORE