Existence of positive S-asymptotically omega-periodic solutions of time-space fractional  nonlocal reaction-diffusion equations

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 \(S\)-asymptotically \(\omega\)-periodic solutions, the existence results of positive \(S\)-asymptotically \(\omega\)-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. For more information see https://ejde.math.txstate.edu/Volumes/2025/44/abstr.html