SPACE-TIME FRACTIONAL HEAT EQUATION'S SOLUTIONS WITH FRACTIONAL INNER PRODUCT

SPACE-TIME FRACTIONAL HEAT EQUATION'S SOLUTIONS WITH FRACTIONAL INNER PRODUCT

S. Cetinkaya, A. Demir

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Abstract

The main goal in this study is to determine the analytic solution of onedimensional initial boundary value problem including sequential space-time fractional di erential equation with boundary conditions in Neumann sense. The solution of the space-time fractional di usion problem is accomplished in series form by employing the separation of variables method. To obtain coe cients 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.

Keywords

Caputo derivative, Mittag-Le er function, Fractional inner product.