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 ...

We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution ...

This paper adapts a new numerical technique for solving twodimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, ...

In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz ...

This paper reports a novel numerical technique for solving the time variable fractional order mobile-immobile advection-dispersion (TVFO-MIAD) model with the Coimbra variable time fractional derivative, which is preferable ...

This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The ...

This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or ...