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In the present work, an attempted was made to develop a numerical algorithmby the use of new orthogonal hybrid functions formed from hybrid of piecewiseconstant orthogonal sample-and-hold functions and piecewise linear orthogonaltriangular functions to obtain the numerical solution of multi-order fractionaldifferential equations. The construction of numerical algorithm involves aformula, consisting of generalized one-shot operational matrices, expressingexplicitly the Riemann-Liouville fractional order integral of the neworthogonal hybrid functions in terms of new orthogonal hybrid functionsthemselves. A set of test problems comprising of linear and nonlinearmulti-order fractional differential equations with constant and variablecoefficients was considered to demonstrate the accuracy and computationalefficiency of our algorithm and to compare our results with those acquired bysome other well-known methods used for solving multi-order fractionaldifferential equations in the literature. The comparison highlighted that ouralgorithm exhibits superior performance to those methods.

Novel hybrid function operational matrices of fractional integration: An application for solving multi-order fractional differential equations