Estimates for a general fractional relaxation equation and application to an inverse source problem
Abstract
A general fractional relaxation equation is considered with a convolutional derivative in time introduced by A. Kochubei (Integr. Equ. Oper. Theory 71 (2011), 583-600). This equation generalizes the single-term, multi-term and distributed-order fractional relaxation equations. The fundamental and the impulse-response solutions are studied in detail. Properties such as analyticity and subordination identities are established and employed in the proof of an upper and a lower bound. The obtained results extend some known properties of the Mittag-Leffler functions. As an application of the estimates, uniqueness and conditional stability are established for an inverse source problem for the general time-fractional diffusion equation on a bounded domain.
Keywords
Cite
@article{arxiv.1802.05464,
title = {Estimates for a general fractional relaxation equation and application to an inverse source problem},
author = {Emilia Bazhlekova},
journal= {arXiv preprint arXiv:1802.05464},
year = {2018}
}