TY - JOUR
AU - Mishura, Yuliya S.
AU - Hopkalo, Olha M.
AU - Zhelezniak, Hanna S.
PY - 2022/04/26
Y2 - 2024/04/12
TI - Elements of fractional calculus. Fractional integrals
JF - Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences
JA - BTSNUKPhM
VL -
IS - 1
SE - Algebra, Geometry and Probability Theory
DO - 10.17721/1812-5409.2022/1.1
UR - https://bphm.knu.ua/index.php/bphm/article/view/298
SP - 11-19
AB - <p><em>The paper is devoted to the basic properties of fractional integrals. It is a survey of the well-</em><em>known properties of fractional integrals, however, the authors tried to present the known information </em><em>about fractional integrals as short and transparently as possible. We introduce fractional integrals on </em><em>the compact interval and on the semi-axes, consider the famous Hardy-Littlewood theorem and other </em><em>properties of integrability of fractional integrals. Among other basic properties, we consider Holder </em><em>continuity and establish to what extent fractional integration increases the smoothness of the integrand. </em><em>Also, we establish continuity of fractional integrals according to the index of fractional integration, both </em><em>at strictly positive value and at zero. Then we consider properties of restrictions of fractional integrals </em><em>from semi-axes on the compact interval. Generalized Minkowsky inequality is applied as one of the </em><em>important tools. Some examples of calculating fractional integrals are provided.</em></p><p><em><strong>Pages of the article in the issue</strong></em>: 11 - 19</p><p><em><strong>Language of the article</strong>: </em>Ukrainian</p>
ER -