Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Abstract

Abstract:In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

Numerical solution for a class of multi-order fractional differential equations with error correction and convergence analysis

“…Compared with [30], Example 1 studies the approximation effect of numerical solution and exact solution, the absolute errors and the absolute error of correct solution. When n = 4, 6, 7, the absolute errors for equation in some match points between the numerical solution and the exact solution are shown in Fig.…”

“…Because there is no exact solution, most different numerical methods, such as stable fractional Chebyshev differentiation matrix [27], fractional-order operational method [28], spectral collocation methods [29], and so on, have been used to investigate the approximate solutions of multiorder fractional differential equation. The authors of [30] only researched the convergence effect of numerical solutions and exact solutions of equations. There is little literature with shifted Chebyshev polynomials to solve multi-order fractional differential equation and research error correction and convergence.…”

Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration

“…Existence, uniqueness and stability of solution for multi-term fractional differential equations are discussed in [45][46][47][48][49]. Because of difficulty of finding the exact solutions for such equations, many new numerical techniques have been developed to investigate the numerical solutions such as Adams method [50], Haar wavelet method [51], differential transform method [52], Adams-Bashforth-Moulton method [53], collocation method based on shifted Chebyshev polynomials of the first kind [54], Boubaker polynomials method [55], matrix Mittag-Leffler functions [56], differential transform method [57] and so on.…”

Existence results in Banach space for a nonlinear impulsive system

“…Mathematical models by using fractional order DEs have been considered in control theory, viscoelastic theory, biology, fluid dynamics, hydrodynamics, image processing, signals, and computer networking. For details, we suggest [1][2][3][4][5][6][7][8].…”