Subordination principle for space-time fractional evolution equations and some applications

2018/12/06 by Bazhlekova, Emilia
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.02421

Abstract

The abstract Cauchy problem for the fractional evolution equation with the Caputo derivative of order β∈(0,1) and operator -A^α, α∈(0,1), is considered, where -A generates a strongly continuous one-parameter semigroup on a Banach space. Subordination formulae for the solution operator are derived, which are integral representations containing a subordination kernel (a scalar probability density function) and a C₀-semigroup of operators. Some properties of the subordination kernel are established and representations in terms of Mainardi function and Lévy extremal stable densities are derived. Applications of the subordination formulae are given with a special focus on the multi-dimensional space-time fractional diffusion equation for some special values of the parameters.

Related

• Completely monotone functions and some classes of fractional evolution equations
• Stochastic solutions for space-time fractional evolution equations on\n bounded domain
• Sobolev spaces and trace theorems for time-fractional evolution equations
• Subordination principle, Wright functions and large-time behaviour for the discrete in time fractional diffusion equation
• Stochastic fractional evolution equations of order 1<α<2 with generalized operators