Approximate controllability Controllability 2 Application of standards 1 Cauchy sequence 1 Controllability problems 1 Fixed point arithmetic 1 Fractional Laplacian 1 Fractional heat equation 1 Gronwall inequality 1 Gronwall's inequality 1 Heat equation 1 Heat transfer 1 Impulse response 1 Impulsive effects 1 Impulsive system 1 Impulsive systems 1 Laplace transforms 1 Lipschitz conditions 1 Lipschitz continuity 1 Numerical aspects 1 Numerical methods 1 One-dimensional 1 One-dimensional heat 1 Partial differential equations 1 Penalized HUM 1 Semi-group theory 1 Semilinear 1 Theoretical aspects 1 controllability 1 fractional Laplacian 1