The construction of operational matrix of fractional integration using triangular functions

In this paper the operational matrix of triangular functions for fractional order integration in the Caputo sense is derived. Also, the operational matrix of fractional integration is applied for solving multi-order fractional differential equations, Abel's integral equations and nonlinear integro-differential equations. This technique is a successful method because of reducing such problems to solve a system of algebraic equations; so, the problem can be solved directly. The advantage of this method is low cost of setting up the equations. Illustrative examples demonstrate accuracy and efficiency of the method.