in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in the Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration f...

Abstract: A numerical technique is presented for the solution of Klein-Gordon equation. This method uses interpolating scaling functions. The method consists of expanding the required approximate solution as the elements of interpolating scaling functions. Using the operational matrix of derivatives, we reduce the problem to a set of algebraic equations. Some numerical examples are included to ...

a simple, novel, efficient and three-component procedure for the synthesis of pyrimido[4,5-d]pyrimidine-2,4-dione derivatives by the reaction of 6-amino-1,3-dimethyluracil, aldehyde and 2-benzylisothiourea hydrochloride promoted by ionic liquid 1-butyl-3-methylimidazolium bromide ([bmim]br) under solvent-free conditions is reported. the presented method is benefited from operational simplicity,...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

The highly substituted pyridine derivatives are found to exhibit diverse pharmacological activities. They are also emerged as potential medicinal leads in developing therapeutic agents for the treatment of various diseases. In this work, a series of 2-amino-3,5-dicarbonitrile-6-thio-pyridine derivatives have been synthesized at room temperature via one-pot, multi-component reaction of various a...

Oxalic acid dihydrate as a green, mild and efficient catalyst for the one-pot three-component Biginelli synthesis of 3,4-dihydropyrimidin-2-(1H)-one derivatives from the reaction between β-keto esters (methyl or ethyl acetoacetate), aromatic aldehyde (benzaldehye derivatives) and urea or thiourea under thermal and solvent-free conditions with excellent yields and short reaction time is st...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...