TY - JOUR ID - 697483 TI - Analytical-Numerical Solution for a Third Order Space-time Conformable Fractional PDE with Mixed Derivative by Spectral and Asymptotic Methods JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Jahanshahi, Mohammad AU - Danaei, Reza AD - Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53714-161, Tabriz, Iran. AD - Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53714-161, Tabriz, Iran. Y1 - 2023 PY - 2023 VL - 20 IS - 1 SP - 81 EP - 93 KW - Asymptotic expansion KW - Analytical-Numerical solution KW - Fractional partial differential equation KW - spectral method DO - 10.22130/scma.2022.550726.1079 N2 - 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. UR - https://scma.maragheh.ac.ir/article_697483.html L1 - https://scma.maragheh.ac.ir/article_697483_b4c31e8ee50eb6ec5ae034967701d4ac.pdf ER -