The operational matrix of Caputo fractional derivatives of modified generalized Laguerre polynomials and its applications

• Published in: Advances in difference equations Vol. 2013; no. 1
• Main Authors: Bhrawy, Ali H, Alghamdi, Mohammed A
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 08.11.2013
• Subjects: Analysis; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; pseudo-spectral approximation; modified generalized Laguerre polynomials; operational matrix; tau method; nonlinear fractional differential equations; Caputo derivative
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2013-307

In this paper, the modified generalized Laguerre operational matrix (MGLOM) of Caputo fractional derivatives is constructed and implemented in combination with the spectral tau method for solving linear multi-term FDEs on the half-line. In this approach, truncated modified generalized Laguerre polynomials (MGLP) together with the modified generalized Laguerre operational matrix of Caputo fractional derivatives are analyzed and applied for numerical integration of such equations subject to initial conditions. The modified generalized Laguerre pseudo-spectral approximation based on the modified generalized Laguerre operational matrix is investigated to reduce the nonlinear multi-term FDEs and their initial conditions to a nonlinear algebraic system. Through some numerical experiments, we evaluate the accuracy and efficiency of the proposed methods. The methods are easy to implement and yield very accurate results.