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

Document Type: Research Paper

Authors

1 School of‎ ‎Mathematics‎, ‎Iran University of Science & Technology‎, ‎Narmak‎, ‎Tehran 16846 13114‎, ‎Iran.

2 Department of Mathematics‎, ‎Faculty of Mathematics‎, ‎Statistics‎ ‎and Computer Sciences‎, ‎Semnan University‎, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.

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.

Keywords

Main Subjects

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### History

• Receive Date: 28 February 2014
• Revise Date: 24 September 2015
• Accept Date: 14 November 2015