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The motivation of this study is to determine the analytic solution of initial boundary value problem including time fractional dierential equation with Neumann boundary conditions in one dimension. By making use of seperation of variables, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.

THE ANALYTIC SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM INCLUDING TIME FRACTIONAL DIFFUSION EQUATION