The fractional calculus has many applications in applied science and engineering. The solution of the differential equation containing fractional derivative is much involved. An effective and easy-to-use method for solving such equations is needed. However not only the analytical solutions exist for a limited number of cases, but also the numerical methods are very complicated and difficult. In...

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

In this paper, we develop an efficient Legend...

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. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

In this paper, an efficient and accurate computational method based on the Chebyshev wavelets (CWs) together with spectral Galerkin method is proposed for solving a class of nonlinear multi-order fractional differential equations (NMFDEs). To do this, a new operational matrix of fractional order integration in the Riemann-Liouville sense for the CWs is derived. Hat functions (HFs) and the collo...