This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.(SPRINGER HEIDELBERG, 2014)
The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional ...
Bhrawy, A. H.; Alofi, A. S.; Ezz-Eldien, S. S.(PERGAMON-ELSEVIER SCIENCE LTD, 2011)
In this article, we develop a direct solution technique for solving multi-order fractional differential equations (FDEs) with variable coefficients using a quadrature shifted Legendre tau (Q-SLT) method. The spatial ...
E. H., Doha; A. H., Bhrawy; S. S., Ezz-Eldien(ELSEVIER SCIENCE INC, 2012)
In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives which is applied together with spectral tau method for numerical solution of general linear multi-term fractional differential ...