quartic and pantic b-spline operational matrix offractional integration

In this work, we proposed an e ective method based on quartic and pantic b-spline scaling functions to solve partial di erential equations of fractional order. our method is based on dual functions of b-spline scaling functions. we derived the operational matrix of fractional integration of quartic and pantic b-spline scaling functions and used them to transform the mentioned equations to a system of algebraic equations. some examples are presented to show the applicability and e ectivity of the technique.