Existence of weak solutions for the nonlocal energy-weighted fractional reaction-diffusion equations

For any bounded smooth domain Omega subset of R-n, we establish the global existence of weak solutions u is an element of L-2(0, T; H-Omega,0(s)) with u(t) is an element of L-2( 0, T; H-Omega(-s)) to the initial boundary value problem of the nonlocal energy-weighted fractional reaction-diffusion equations for any initial data u(0) is an element of H-Omega,0(s).