References 1. Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA (2015) New Operational Matrices for Solving Fractional Differential Equations on the Half-Line. PLoS ONE 10(5): e0126620. doi: 10.1371/ journal.pone.0126620 PMID: 25996369 2. Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA (2015) Correction: New Operational Matrices for Solving Fractional Differential Equations on...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The solution takes the form product consisting unknown coefficients and polynomials. Our main task is compute numerical values coefficients. To achieve goal, apply initial condition problem, Tau Lagrange multiplier methods. We do error ana...

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is basically built on transforming the eq...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...