Analytical solution of the Bagley Torvik equation by Adomian decomposition method

Numerical method for fractional dispersive partial differential equations

“…In order to attain the aim of extremely accuracy and consistent solutions, numerous approaches have been suggested to crack the fractional order differential equations. Some of the current analytical/numerical methods are Adomian decomposition method (ADM) [15][16][17][18][19][20], finite difference method [21], Operational matrix method [22], Homotopy analysis method [23,-24], generalized differential transform method [25,26], finite element method [27], fractional differential transform method [28][29] and references therein. http://www.ispacs.com/journals/cna/2017/cna-00266/ International Scientific Publications and Consulting Services…”

Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

“…In the literature, equation (1) is called the Bagley-Torvik equation. A numerical solution of problem (1)- (2) is given in [11,12] and analytical solutions in [10,13]. Papers [2,4,7,8] …”

Analytical Approximation for Fractional Order Logistic Equation

“…Most fractional differential equations do not have exact analytic solutions and consequently, approximate analytical and numerical techniques are required to solve the fractional differential equations. Approximate analytical solution techniques for FDEs such as variational iteration method [2], operational matrix method [3,4,5], Adomian decomposition method [6,7], homotopy perturbation method [8,9,10,11], tau method [12], collocation method [13,14,15], homotopy analysis method [16,17,18,19,20], and optimal homotopy analysis method [21] have been developed. A fractional logistic model can be obtained through the application of fractional derivative operator on the logistic equation.…”