6533b831fe1ef96bd1298fce

RESEARCH PRODUCT

Step-by-step integration for fractional operators

Natalia Colinas-armijoMario Di Paola

subject

Numerical AnalysisDiscretizationApplied Mathematics02 engineering and technologyFunction (mathematics)DerivativeWhite noise01 natural sciences010305 fluids & plasmasExponential functionFractional calculus020303 mechanical engineering & transports0203 mechanical engineeringModeling and SimulationStep function0103 physical sciencesPiecewiseApplied mathematicsFractional Calculus Riemman–Liouville Grünwald–Letnikov Discrete fractional operatorsMathematics

description

Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and the Grunwald–Letnikov discrete operators, both techniques have been applied to: unit step functions, exponential functions and sample functions of white noise.

yearjournalcountryeditionlanguage
2018-06-01
10.1016/j.cnsns.2017.11.030http://hdl.handle.net/10447/249721