Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods

The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

“…Using a complete discrimination system for polynomial to classify the roots of ( ), we solve (12) with the help of Mathematica7 and classify the exact solutions to (7). In addition, we can write the exact traveling wave solutions to (5), respectively.…”

“…Also, a remarkable progress has been become in the construction of the approximate solutions for fractional nonlinear partial differential equations [1][2][3]. Several powerful methods [4][5][6][7][8][9][10][11][12][13] have been proposed to obtain approximate and exact solutions of fractional differential equations, such as the Sumudu transform method, the Homotopy analysis method, and the homotopy perturbation method.…”

Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem

“…Therefore, from (14), (15) and (16) the following relation is obtained then, we have finally Omitting the small term ℜ (n− 1 2 ) and replacing u (n) with its numerical approximation ũ (n) , the following discretized scheme is obtained Using (5) and rearranging the Eq. (20), the following equivalent time-discretized relation at nth time level is obtained (17)…”

“…Recently, the time-fractional Tricomi-type equation by replacing the second-order time derivative with Caputo fractional derivative of order (1 < ≤ 2) is proposed. In [15], a one-dimensional time-fractional Tricomi-type problem has been introduced and a local discontinuous Galerkin finite element technique is formulated and applied for solving the problem. Zhang et al [16] investigated a two-dimensional time-fractional Tricomi-type equation by using the finite element method.…”

Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics

“…For the numerical solution of the TFTTM, we find some works published during the last years. Zhang et al [5] formulated a local discontinuous Galerkin finite element, Zhang et al [6] used the finite element scheme and Liu et al [7] applied the reduced-order finite element technique to approximate the TFTTM. More recently, Dehghan and Abbaszadeh [8] adopted the element-free Galerkin technique and Ghehsareh et al [9] implemented the local Petrov–Galerkin formulation.…”