Electron. J. Differential Equations, Vol. 2025 (2025), No. 44, pp. 1-15.
Existence of positive S-asymptotically omega-periodic solutions of time-space fractional nonlocal reaction-diffusion equations
Xuping Zhang, Kaibo Ding, Pengyu Chen
Abstract:
This article studies the asymptotically periodic problem of
time-space fractional reaction-diffusion equations with nonlocal
initial conditions on infinite intervals. Without the assumption of
upper and lower -asymptotically -periodic solutions,
the existence results of positive -asymptotically
-periodic solutions for a class of abstract time-space
fractional evolution equations with nonlocal initial conditions
under growth and order conditions are obtained by using the theory
of operator semigroups and the method of monotone iteration.
Finally, the abstract results were applied to time-space fractional
reaction-diffusion equations with nonlocal initial conditions and
some new results were obtained.
Submitted July 13, 2024. Published April 24, 2025.
Math Subject Classifications: 35R11, 35B09, 34G20, 47J35.
Key Words: Time-space fractional reaction-diffusion equation;
nonlocal initial conditions; positive S-asymptotically
omega-periodic mild solutions; monotone iterative technique.
DOI: 10.58997/ejde.2025.44
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Xuping Zhang
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: lanyu9986@126.com
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Kaibo Ding
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: dingkb583x@163.com
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Pengyu Chen
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China.
email: chpengyu123@163.com
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