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Abstract
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Initial-boundary value problems including space-time
fractional PDEs have been used to model a wide range of problems
in physics and engineering fields. In this paper, a non-self adjoint
initial boundary value problem containing a third order fractional
differential equation is considered. First, a spectral problem for this
problem is presented. Then the eigenvalues and eigenfunctions of
the main spectral problem are calculated. In order to calculate the
roots of their characteristic equation, the asymptotic expansion of
the roots is used. Finally, by suitable choice of these asymptotic
expansions, related eigenfunctions and Mittag-Lefler functions, the
analytic and numerical solutions to the main initial-boundary value
problem are given.
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