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Green’s function of time fractional diffusion equation and its applications in fractional quantum mechanics. (English) Zbl 1167.35441
Summary: Fractional equations, which have derivatives of noninteger order, are very successful in describing anomalous kinetics, transport, and chaos. To obtain the exact solutions of these equations, we need to find a more valid analytical method. In this paper, we propose a new technique for solving a class of time fractional partial differential equations. Then this method is successfully applied to find the Green’s functions; emphasis in the applications is given to the questions in anomalous diffusion and the time Schrödinger equation.
35Q40PDEs in connection with quantum mechanics
35A08Fundamental solutions of PDE
26A33Fractional derivatives and integrals (real functions)
81Q99General mathematical topics and methods in quantum theory