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Title
Solving Two Initial-Boundary Value Problems Including Fractional Partial Di erential Equations By Spectral and Contour Integral Methods
Type of Research Article
Keywords
initial-boundary value problem, fractional partial di eren- tial equation, spectral problem, contour integral, closed contour.
Abstract
Initial-boundary value problems including fractional partial di erential equa- tions are the mathematical models of physical problems and natural phenomena. In this paper, at rst we consider a fractional partial di erential equation which has no mixed term derivative with respect to spatial and time variable. We rst consider the spectral problem, then its eigenvalues and eigenfunctions are calculated. After that the eigen- values and eigenfunctions of the adjoint problem are calculated. By using these eigen- functions and Mittag-Leer functions the approximate solution is constructed. In second section, we consider di erential equation which has a mixed term derivative. In this case, by using Laplace transformation, the analytic solution and approximate solution are cal- culated as integral expression over suitable closed contours by contour integral method. At the end, some examples are presented for several cases of di erent distributions of eigenvalues in complex plane.
Researchers Mohammad Jahanshahi (First Researcher)، Nihan Aliev (Second Researcher)، (Third Researcher)