Kronecker operational matrices for fractional calculus and some applications

The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

A numerical method for solving boundary value problems for fractional differential equations

Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions

This paper introduces an approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and Block-Pulse functions. These hybrid functions and their operational matrices are used for representing matrix form of these equations. The main characteristic of this approach is that it reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem. Numerical examples illustrate the validity and applicability of the proposed method.

H. Khatami

Papers

Numerical solution of integral equations system of the second kind by block-pulse functions