TY - JOUR
T1 - On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions
AU - Chen , Pengyu
AU - Gao , Peng
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 791
EP - 807
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.791
UR - https://global-sci.org/intro/article_detail/jnma/21913.html
KW - Time-space fractional reaction-diffusion equation, Nonlocal initial condition, Mild solution, Existence and uniqueness, Mittag-Leffler-Ulam stability.
AB - <p style="text-align: justify;">This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator
semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of
mild solution to the reaction-diffusion equation are obtained by solving the
abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with
nonlocal initial conditions. The results in this paper improve and extend some
related conclusions to this topic.</p>