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Regularity results for fractional diffusion equations involving fractional derivative with Mittag–Leffler kernel
Author(s) -
Tran Bao Ngoc,
Baleanu Dumitru,
Le Thi Minh Duc,
Nguyen Huy Tuan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6459
Subject(s) - mathematics , fractional calculus , mittag leffler function , uniqueness , kernel (algebra) , mathematical analysis , derivative (finance) , anomalous diffusion , boundary value problem , order (exchange) , pure mathematics , innovation diffusion , knowledge management , finance , computer science , financial economics , economics
This paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag–Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is analyzed and considered. The fractional derivative with Mittag–Leffler kernel or also called Atangana and Baleanu fractional derivative in time is taken in the Caputo sense. We obtain results on the existence, uniqueness, and regularity of the solution.