The solution of the Bagley–Torvik equation with the generalized Taylor collocation method

An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem

“…BTB was discussed analytically in [27]. Then, several numerical approaches were used to solve it such as the discrete spline method [28], the Hybridizable discontinuous Galerkin method [29], generalizing the Taylor collocation method [30], and the operational matrix of Haar wavelet method [30]. Special attention was given when y(0) = y(1) = 0.…”

A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

“…Numerical solutions for various types of FDEs by applying several techniques were proposed, for instance, Adomian's decomposition method [2,3], the Taylor collocation method [4], the variational iteration method [5], the finite difference method [6,7] and the ultraspherical wavelets method [8,9]. In addition, orthogonal polynomials have been widely used for obtaining numerical solutions for different types of FDEs.…”

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

“…Staněk together with the initial conditions (0) = 0 (0) = 0 (2) where D 3/2 is the Riemann-Liouville fractional derivative of order 3/2, A = 0 and are constants, and is a function. The authors solved problem (1)- (2) by the Laplace transformation. 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] …”

“…Papers [2,7] state numerical solutions of problem (3) for α = 3/2 while [8] for α ∈ (1 2). In [4], analytical solutions of (3) are discussed in [1].…”