Progress in Fractional Differentiation & Applications

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This paper presents new operational matrices of fractional integral and derivatives for shifted Legendre polynomials. These operational matrices are employed to design a new spectral method for solving three-dimensional heat conduction problem. The main advantage of the proposed method is to reduce this complicated problem with its initial and boundary conditions into a system of easily solvable algebraic equations. The efficiency of the proposed method is shown with some test problems. The results are displayed graphically.

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