Title INVESTIGATION AND SOLVING TWO INITIAL - BOUNDARY PROBLEMS INCLUDING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS BY SPECTRAL AND CONTOUR INTEGRAL METHODS Type of Research Presentation Keywords Initial-Boundary Value Problem, Spectral Problem, Contour Integral, closed contour. Abstract In this paper, at fi rst we consider an intial- boundary value problemwhich contains a fractional partial di erential equation by some intial and boundary conditions by spectral and contour integral method. Researchers Mohammad Jahanshahi (First Researcher)، (Second Researcher)