A Novel Technique for Fractional Bagley–Torvik Equation

An exponential spline approximation for fractional Bagley–Torvik equation

“…The maximum absolute errors in solutions of the methods are tabulated in tables. We compute the absolute error for examples and compare them with the methods in [4,9,17,21,28,29]. The convergence order (C.O.)…”

“…The numerical solutions are computed by Methods I and IV. In order to compare the solutions with [21] in Table 9, we have taken n = 10, 20, and 40 in Table 8. The absolute error and the order of convergence for n = 4, 8, 16, 32, 64, 128, 256, and 512 are given in Table 10.…”

“…The convergence analyses of the shifted Grünwald difference and the exponential spline are discussed. The feasibility of the numerical algorithms was illustrated with four examples, and the approximated results were compared with the methods in [4,9,17,21,28,29].…”

“…reproducing kernel method is employed for the fractional order differential equations in [1][2][3]. In [21], numerical solution of boundary value problem of fractional Bagley-Torvik equation is given in the reproducing kernel space. In [14], the authors study the numerical approach based on operational matrices of fractional differential equations with a hybrid of block-pulse functions and Chebyshev polynomials.…”

“…In Sect. 4, the numerical examples are given to illustrate the applications of the method, and also the computed results are compared with another known method in [4,9,17,21,28,29].…”