On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions (Journal of Nonlinear Modeling and Analysis, 2024)
This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operatorsemigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness ofmild solution to the reaction-diffusion equation are obtained by solving theabstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations withnonlocal initial conditions. The results in this paper improve and extend somerelated conclusions to this topic.
Keywords: Time-space fractional reaction-diffusion equation; Nonlocal initial condition; Mild solution; Existence and uniqueness; Mittag-Leffler-Ulam stability.