An exponential spline approximation for fractional Bagley–Torvik equation

Abstract

In this paper, we approximate the solution of fractional Bagley-Torvik equation by using the exponential spline function and the shifted Grünwald difference operator. The proposed methods reduce to the system of algebraic equations. The convergence analysis of the methods has been discussed. The numerical examples are presented to illustrate the applications of the methods and to compare the computed results with the other methods.

Applied Mathematics and Fractional Calculus

“…In the proposition below, we describe the inverse operator (1 + T q ) −1 connected to the intermediate Equation (56). We omit the proof as it is a straightforward corollary of Theorem A1, and the full proof is analogous to that of Proposition 4.…”

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

“…Table 1 A brief literature review of numerical solver for FBTMM Index Method Remarks [11] in Podlubny's consecutive approximation Novel numerical solution [12] in Deterministic numerical scheme Convergence established [13] in Differential transform method Novel numerical solver [14] in Adomian decomposition method Novel analytical solution [15] in He's variational iteration method Viable analytic method [16] in Matrix approach of discretization Novel discretization [17] in Shooting collocation approach Efficient scheme [18] in Taylor collocation method Power series approach [19] in Genetic algorithms and neural networks Novel stochastic solver [20] in Neural networks and Swarm intelligence Viable stochastic solver [20] in Haar wavelets operational matrix Novel wavelets approach [22] in Sequential quadratic programing Fractional neural network [23] in Interior-point method Fluid dynamics problem [24] in Galerkin approximations Numerical scheme [25] in Exponential spline approximation Novel spline method [26] in Jacobi collocation methods Power series approach [27] in Generalized Bessel polynomial Power series method [28] in Quadratic finite element mentod Numerical computing [29] in Lie symmetry analysis method Numerical analysis…”

Nonpolynomial Spline Interpolation for Solving Fractional Subdiffusion Equations

“…e author of [23] has presented an implicit numerical method for the fractional di usion equation, where the fractional derivative is discretized by spline and the Crank-Nicolson discretization is used for the time variable. e authors of [24] have developed a novel nonpolynomial spline method for solving second-order hyperbolic equations, and their results are numerically more accurate than some nite di erence methods, see [25][26][27][28]. e authors of [29] presented a quadratic nonpolynomial spline approach to approximate the solution of a system of second-order boundary value problems associated with a one-sided obstacle, and compared to collocation, nite di erence, and certain common polynomial spline approaches, we used contact problems and produced approximations that were more accurate.…”