# Exponentially convergent method for an abstract integro - differential equation with fractional Hardy - Titchmarsh integral

 Title Exponentially convergent method for an abstract integro - differential equation with fractional Hardy - Titchmarsh integral Publication Type Journal Article Year of Publication 2021 Authors Makarov, VL, Gawriljuk, IP, Vasylyk, VB Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2021.01.003 Issue 1 Section Mathematics Pagination 3-8 Date Published 2/2021 Language Ukrainian Abstract A homogeneous fractional-differential equation with a fractional Hardy—Titchmarsh integral and an unbounded operator coefficient in a Banach space is considered. The conditions for the representation of the solution in the form of a Danford—Cauchy integral are established, and an exponentially convergent approximation method is developed. Keywords differential equation with fractional derivatives, exponentially convergent method, unbounded operator
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