مشخصات پژوهش

صفحه نخست /Solving Two Initial-Boundary ...
عنوان
Solving Two Initial-Boundary Value Problems Including Fractional Partial Di erential Equations By Spectral and Contour Integral Methods
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
initial-boundary value problem, fractional partial di eren- tial equation, spectral problem, contour integral, closed contour.
چکیده
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.
پژوهشگران محمد جهانشاهی (نفر اول)، نیهان علی اف (نفر دوم)، فاطمه جهانشاهی خضرلو (نفر سوم)