Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902005 | Journal of Computational and Applied Mathematics | 2018 | 21 Pages |
Abstract
This paper is concerned with the fractional evolution equation with a discrete distribution of Caputo time-derivatives such that the largest and the smallest orders, α and αm, satisfy the conditions 1<αâ¤2 and αâαmâ¤1. First, based on a study of the related propagation function, the nonnegativity of the fundamental solutions to the spatially one-dimensional Cauchy and signaling problems is proven and propagation speed of a disturbance is discussed. Next, we study the equation with a general linear spatial differential operator defined in a Banach space and suppose it generates a cosine family. A subordination principle is established, which implies the existence of a unique solution and gives an integral representation of the solution operator in terms of the corresponding cosine family and a probability density function. Explicit representation of the probability density function is derived. The subordination principle is applied for obtaining regularity results. The analytical findings are supported by numerical work.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Emilia Bazhlekova, Ivan Bazhlekov,