Canonical Quantization for Fractional Schrödinger Lagrangian Density in Caputo Definition

The fractional form of the Schrodinger Lagrangian density is presented using the Caputo's fractional derivative. Agrawal procedure is employed to obtain time dependent and time independent Schrodinger equations in Caputo's fractional form. The Hamiltonian density resulting from the Schrodinger Lagrangian density is obtained in fractional form. Then, we used Dirac algebraic method to quantize the Schrodinger Lagrangian density by determining the fractional creation and annihilation operators and constructing the fractional Canonical Commutation Relations (CCRs).