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

Keywords: differential equation with fractional derivatives, unbounded operator, xponentially convergent method

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.

References

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Hardy, G. H. & Titchmarsh, E. C. (1932). An integral equation. Math. Proc. Camb. Philos. Soc., 28, Iss. 2, pp. 165-173. https://doi.org/10.1017.SO305004100010847

Gavrilyuk, I., Makarov, V. & Vasylyk, V. (2011). Exponentially convergent algorithms for abstract differential equations. Frontiers in Mathematics. Basel: Birkhäuser/Springer Basel AG. https://doi.org/10.1007/978-3-0348-0119-5

Stenger, F. (1993). Numerical methods based on sinc and analytic functions. New York: Springer. https://doi.org/10.1007/978-1-4612-2706-9

Published
2021-03-23
How to Cite
Makarov, V., Gawriljuk, I., & Vasylyk, V. (2021). Exponentially convergent method for an abstract integro - differential equation with fractional Hardy - Titchmarsh integral . Reports of the National Academy of Sciences of Ukraine, (1), 3-8. Retrieved from http://ojs.akademperiodyka.org.ua/index.php/dopovidi/article/view/dopovidi2021.01.003