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.
Khalil, Hammad and Ali Khan, Rahmat
"Extended Spectral Method for Fractional order Three-dimensional Heat Conduction Problem,"
Progress in Fractional Differentiation & Applications: Vol. 1
, Article 3.
Available at: https://dc.naturalspublishing.com/pfda/vol1/iss3/3