Abstract
Herein, an innovative operational matrix of fractional-order derivatives (sensu Caputo) of Fermat polynomials is presented. This matrix is used for solving the fractional Bagley-Torvik equation with the aid of tau spectral method. The basic approach of this algorithm depends on converting the fractional differential equation with its initial (boundary) conditions into a system of algebraic equations in the unknown expansion coefficients. The convergence and error analysis of the suggested expansion are carefully discussed in detail based on introducing some new inequalities, including the modified Bessel function of the first kind. The developed algorithm is tested via exhibiting some numerical examples with comparisons. The obtained numerical results ensure that the proposed approximate solutions are accurate and comparable to the analytical ones.
Highlights
Fractional-order calculus is a vital branch of mathematical analysis
Many practical problems in various fields such as mechanics, engineering and medicine are modeled by fractional differential equations
We have developed a new operational matrix of fractional derivatives of Fermat polynomials
Summary
Fractional-order calculus is a vital branch of mathematical analysis. Many practical problems in various fields such as mechanics, engineering and medicine are modeled by fractional differential equations. The tau method is a synonym for expanding the residual function as a series of orthogonal polynomials and applying the boundary conditions as constraints. The use of operational matrices of different orthogonal polynomials jointly with spectral methods produces efficient, accurate solutions for such equations (see, for example, [ – ]). To establish a new operational matrix of fractional derivatives of Fermat polynomials.
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