Improved estimates for separation of solutions to fractional differential equations
Người báo cáo: TS. Nguyễn Như Thắng (Đại học Sư Phạm Hà Nội)

Thời gian: 9h30 ngày 21 tháng 06 năm 2022

Địa điểm: 302-A5, Viện Toán học

Tóm tắt: In this talk, we examine the upper and lower bounds for separation of two solutions to certain fractional differential equations. By investigating the commutator of the translation operator and the Caputo fractional derivatives, we establish the short-term memory phenomenon, which sharpens the recent Diethelm-Tuan's result in Fract. Calc. Appl. Anal. (2022). As by-product, we obtain the sub/super multiplicative properties of Mittag-Leffler functions, which play an essential role in global Halanay type inequality approach. Furthermore, by utilizing the estimate of the commutator, we prove the upper bound with exact decaying rate for separation of solution to delay fractional equations under a flexible /eventually stable condition. Consequently, we gain a practical sufficient criterion for strict Mittag-Leffler stability for a class of delay fractional equations. Some concrete examples are examined to compare these results with the known ones.

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