Boundary particle method for Laplace transformed time fractional diffusion equations

► Error analysis and numerical experiments demonstrate the efficiency of our method for time fractional diffusion equations. ► Our method avoids costly convolution integral calculation and dilemmatic selection of time step size. ► A truly boundary-only meshless method is applied to Laplace-transformed inhomogeneous problem. ► Our method effectively simulates 3D long time-history fractional diffusion systems.