A new approach for solving a system of fractional partial differential equations

Exact solutions for linear systems of local fractional partial differential equations

“…From the equations (4.7)-(4.8), the first solution terms of local fractional sumudu decomposition method of the system (4.1), is given by This obtained result is the same as in the article [31] in the case α = β = 1, as well as the same result presented in the article [32] in the same case.…”

Oscillation properties for solutions of a kind of partial fractional differential equations with damping term

“…Consider the following partial fractional differential equation 6) with the boundary condition u(0, t) = u(π, t) = 0, t > 0. (5.7)…”

“…Jafari et al [6] presented the iterative Laplace transform method to derive exact and approximate analytical solutions of fractional partial differential equations. Chen and Jiang [2] exploited the techniques of Lie group analysis to solve n-order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation.…”

Analytic solution of homogeneous time-invariant fractional IVP

“…Almost all attempts were developed by either finding nu-merical solutions over a specific range or considering few terms of an iterative computational series solution as an approximate. Such available methods are (He's) variational iteration methods [11,12], the iterative Laplace transform method [13], Adomian's decomposition method [14], the differential transform method [15,16], homotopy analysis/perturbation methods [17,18], the homotopy analysis-Laplace transform method [19], Chebyshev/Jacobi/Legendre operational matrix methods [20], the fractional Lie group method [21], the generalized Taylor power series method [22,23], and the residual power series method [24][25][26][27][28].…”