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Existence of periodic and S‐asymptotically periodic solutions to fractional diffusion equations with analytic semigroups
Author(s) -
Mu Jia,
Nan Jiecuo,
Zhou Yong
Publication year - 2021
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.5895
Subject(s) - mathematics , fractional calculus , stability theory , mathematical analysis , diffusion , nonlinear system , physics , quantum mechanics , thermodynamics
In this paper, we study periodic and S‐asymptotically periodic solutions for fractional diffusion equations (FDE). As we all know, there is no exact periodic solution to differential equations with Caputo or Riemann‐Liouville fractional derivatives. Even so, in this paper, periodic (S‐asymptotically periodic) mild or classical solutions for FDE with Weyl‐Liouville fractional derivatives could be obtained in various fractional power spaces. In addition, a numerical simulation example and a specific example of fractional diffusion equation are given to verify the main theoretical results.