Inverse problem for a time-fractional differential equation with a time- and space-integral conditions

Mokhtar Kirane, Andriy Lopushansky, Halyna Lopushanska

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    1 Scopus citations

    Abstract

    We study the inverse problem for a differential equation of order (Figure presented.) with the time Caputo fractional derivative and a source with values in Schwartz-type distributions. The generalized solution of the Cauchy problem for such an equation with initial values and a time-dependent reaction coefficient are unknown. We find sufficient conditions for the unique solvability of the inverse problem under a time- and space-integral overdetermination conditions.

    Original languageBritish English
    Pages (from-to)16381-16393
    Number of pages13
    JournalMathematical Methods in the Applied Sciences
    Volume46
    Issue number15
    DOIs
    StatePublished - Oct 2023

    Keywords

    • fractional derivative
    • Green vector-function
    • integral condition
    • inverse problem
    • Schwartz distribution

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