Subordination principle for space-time fractional evolution equations and some applications. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Bazhlekova, Emilia
• Is Part Of: Integral transforms and special functions. Volume 30:Issue 6(2019)
• Page Start: 431
• Page End: 452
• Publication Date: 2019-06-03
• Subjects: space-time fractional diffusion equation -- fractional Laplacian -- Mittag-Leffler function -- Mainardi function -- Tricomi's confluent hypergeometric function; 26A33 -- 33E12 -- 35R11 -- 47D06; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2019.1581186
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: The abstract Cauchy problem for the fractional evolution equation with the Caputo derivative of orderβ ∈ ( 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 aC 0 -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.