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This paper is devoted to study a computation scheme to approximate solution of fractional differential equations (FDEs) and coupled system of FDEs with variable coefficients. We study some interesting properties of shifted Legendre polynomials and develop a new operational matrix. The new matrix is used along with some previously derived
results to provide a theoretical treatment to approximate the solution of
a generalized class of FDEs with variable coefficients. The new method
have ability to convert fractional order differential equations having variable coefficients to system of easily solvable algebraic equations. We
gave some details to show the convergence of the scheme. The efficiency
and applicability of the method is shown by solving some test problems.
To show high accuracy of proposed method we compare out results withsome other results available in the literature. The proposed method is
computer oriented. We use M atLab to carry out necessary calculations.
Hammad Khalil, Rahmat Ali Khan, Mohammed H. Al-Smadi, Asad A. Freihat, Nabil Shawagfeh. (2015) New Operational Matrix For Shifted Legendre Polynomials and Fractional Differential Equations With Variable Coefficients, Punjab University Journal of Mathematics, Volume 47, Issue 1.
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