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Abstract In this study, an efficient numerical scheme based on shifted Chebyshev polynomials is established to obtain numerical solutions of the Bagley–Torvik equation. We first derive the shifted Chebyshev operational matrix of fractional derivative. Then, by the use of these operational matrices, we reduce the corresponding fractional order differential equation to a system of algebraic equations, which can be solved numerically by Newton’s method. Furthermore, the maximum absolute error is obtained through error analysis. Finally, numerical examples are presented to validate our theoretical analysis.

A numerical scheme based upon the Chebyshev polynomials and collocation method is modified and developed to deal with a class of Volterra integro-differential equations. First, we construct the operational matrices of derivative and pantograph. Then these obtained matrices are then utilized to convert the problems to a system of algebraic equations. Furthermore, we establish a detailed convergence analysis in the weighted square norm. Finally, three numerical experiments are implemented and discussed to confirm the applicability and accuracy of the introduced computational scheme. [ABSTRACT FROM AUTHOR]

In this paper, we suppose and analyze a differential quadrature method for the numerical solution of fractional Logistic differential equation. The fractional derivative is described in the Caputo sense. Explicit expressions of weighting coefficients for approximation of fractional derivatives are derived and are utilized to reduce the Logistic differential equation to system of algebraic equations. The convergence order of the proposed method is investigated in the infinity norm. Numerical examples are presented to verify the efficiency and accuracy of the proposed method. The results reveal that the method is accurate and easy to implement. [ABSTRACT FROM AUTHOR]