Study on multi-order fractional differential equations via operational matrix of hybrid basis functions

Abstract

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 ‎convergence of the approximate solutions is considered‎. ‎The‎ ‎numerical results obtained by this scheme have been compared with‎ ‎the exact solution to show the efficiency of the method‎.