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arXiv · 1802.05464

Estimates for a general fractional relaxation equation and application to an inverse source problem

Emilia Bazhlekova
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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.

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Emilia Bazhlekova. 2018-02-15. Estimates for a general fractional relaxation equation and application to an inverse source problem. https://doi.org/10.1002/mma.4868

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