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

In this paper we apply hybrid functions of general block-pulseý ýfunctions and Legendre polynomials for solving linear andý ýnonlinear multi-order fractional differential equations (FDEs)ý. ýOur approach is based on incorporating operational matrices ofý ýFDEs with hybrid functions that reduces the FDEs problems toý ýthe solution of algebraic systemsý. ýError estimate that verifies aý ýconvergence of the approximate solutions is consideredý. ýTheý ýnumerical results obtained by this scheme have been compared withý ýthe exact solution to show the efficiency of the methodý.