In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear m...

In this work, a new approach of the Kekre transform in the integral form is introduced. A theory of operation matrix is developed by numerical computation and by partitioning of the matrices in four submatrices which is proved as the same. An operational matrices of integration based on Kekre transform are applied to the dynamic systems with distributed parameters to analyse their applications....

The so-called modified transform (T) graphs are described in the paper, which are a graph analogy to wellknown voltage and current incidence matrices. The procedure is shown how to pass from T-graphs to the classical Mason-Coates (MC) flow graph. The explanation is illustrated with examples of circuits containing operational amplifiers and current conveyors. Key-Words: Signal flow graph, flow g...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

One-dimensional parabolic equation; Nonlocal boundary conditions; Taylor approximation; Operational matrices; Krylov subspace iterative methods; Restarted GMRES Abstract This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs) subject to nonlocal boundary integral c...

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and ...