Space-time fractional heat equation’s solutions with fractional inner product

Abstract

The main goal in this study is to determine the analytic solution of onedimensional initial boundary value problem including sequential space-time fractional differential equation with boundary conditions in Neumann sense. The solution of the space-time fractional diffusion problem is accomplished in series form by employing the separation of variables method. To obtain coefficients in the Fourier series is utilized a fractional inner product. The obtained results are supported by an illustrative example. Moreover, it is observed that the implementation of the method is straightforward and smooth.