OPTIMIZATION ALGORITHM FOR NUMERICAL IMPLEMENTATION OF THE FRACTIONAL GRUNWALD-LETNIKOV DERIVATIVE BASED ON THE MEMORIZATION PRINCIPLE FOR ORDINARY DIFFERENTIAL EQUATIONS

Fractional derivatives, due to their nonlocality, can describe complex processes where historical data are important for future calculations. At the same time, this property brings difficulties in numerical simulations. This paper presents a new discrete operator for approximating the fractional derivative based on the Grunwald-Letnikov definition, the "principle of short memory", memorization and analytical assumptions. This operator significantly reduces the number of operations in the process of calculations, when solving boundary value problems, due to the storage of calculated data and transformation for further use with adjustable accuracy. 

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