Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation

Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method

“…It is clear that the results using the DTM have a reasonable agreement with the results obtained using only the fourth-order Runge-Kutta numerical method in a small range of the solution domain. Now we are improving the accuracy of the differential transform solution using the MDTM [22]. We first apply Laplace transform to the series solution given by Equation (12) …”

“…This is a powerful method for solving linear and nonlinear differential equations. This method was at first used as differential transform method in the engineering domain by Zhou [17] and in fluid flow problems [18][19][20][21][22][23][24][25]. The differential transform solution diverges by using finite number of terms.…”

Hermite Solution of Bagley-Torvik Equation of Fractional Order

“…Many technics have been delegated to solve differential equation of fractional order. Different structures are used to resolve the issues of nonlinear physical models of fractional orders like Finite element method [1], Finite difference method [2], differential transformation method [3] [4], Adomian's decomposition method [5] [6] [7], variational iteration method [8] [9] [10], Homotopy perturbation technique [11], Zubair decomposition method (ZDM) [12], (G'/G)-expansion method [13], (U'/U)-expansion method [14], Uexpansion method [15], Fractional sub numerical announcement method [16] [17], Legendre wavelets technique [18], Chebyshev wavelets framework [19] [20] [21], Haar wavelets schema [22], Legendre Method [23], Chebyshev strategy [24], Jacobi polynomial scheme [25] and collocation scheme [26] [27] [28] [29]. All the mentioned approaches have certain limitations like excessive computational work, less efficiency to tackle nonlinearity and divergent solution due to which many issues arise.…”

Determination of an unknown source term for an inverse source problem of the time-fractional equation

“…Because of the nonlocal and non-commutative nature of fractional derivative, it becomes a powerful tool to describe various physical processes and phenomena with the properties of memory and hereditary [3,24]. In recent years, the subject of fractional calculus have attracted the attentions of many researchers and are becoming increasingly popular due to their practical applications in various fields of science and engineering [28,7,18]. There are many different types of definitions of fractional calculus.…”