Solution of Sakata-Taketani Equation via the Caputo and Riemann-Liouville Fractional Derivatives

Abstract

In this paper, we present the Sakata–Taketani (ST) equation of spin 0 in the framework of fractional derivatives . We propose fractional Lagrangian and Hamiltonian densities. Using the fractional variational principle , the fractional Sakata–Taketani equation and its adjoint are determined. Accordingly, we have solved exactly the following problems: the free Sakata-Taketani equation of spin 0 in both cases (in time fractional and in space-time fractional cases) and the Sakata–Taketani particle of spin 0 in space-time fractional and in a box model (also known as the infinite potential well).