gives a numerical approximation to the Riemann–Liouville fractional derivative of order α of the function f at the point x0.
Details and Options
- NFractionalD is the numerical analog of FractionalD, also known as the Riemann–Liouville differintegral of f.
- The Riemann–Liouville fractional derivative of of order is defined as , where .
- NFractionalD is typically used in cases when symbolic evaluation with FractionalD fails.
- The following options can be given to NFractionalD:
Method Automatic method to use AccuracyGoal Infinity digits of absolute accuracy sought PrecisionGoal Automatic digits of precision sought WorkingPrecision MachinePrecision the precision used in internal computations
- The following Method option settings may be used:
Automatic automatically selected method "GrunwaldLetnikov" Grünwald-Letnikov fractional differintegration scheme "RiemannLiouville" Riemann-Liouville fractional differintegration scheme
Examplesopen allclose all
Basic Examples (5)
Numerical fractional derivative of MittagLefflerE at a point:
Generate a list of numerical values of the fractional derivative of the MittagLefflerE function:
Calculate the 0.23-order fractional derivative of the Exp function numerically and symbolically:
Calculate the value of the half-order derivative of the ArcTan function at some point:
The -order fractional derivative of the Sin function:
The -order fractional integral of the Sin function:
The half-order fractional derivative of the AiryAi function:
Numerically calculate the fractional derivative of the BesselJ function:
Numerically calculate the fractional derivative of the MeijerG function:
NFractionalD has two built-in methods, the Riemann–Liouville and the Grünwald–Letnikov methods:
For a specific order of fractional differentiation, this is a cumbersome sum of HypergeometricPFQ functions:
Effectively generate a list of numerical values of fractional derivatives of a complex function using NFractionalD:
Properties & Relations (6)
NFractionalD is defined for all real :
Plot the fractional derivative using the numerical NFractionalD approach:
Compare with the symbolic FractionalD approach:
Possible Issues (3)
Neat Examples (1)
Plot the Sin function and its half, first and -order derivatives:
Wolfram Research (2022), NFractionalD, Wolfram Language function, https://reference.wolfram.com/language/ref/NFractionalD.html.
Wolfram Language. 2022. "NFractionalD." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NFractionalD.html.
Wolfram Language. (2022). NFractionalD. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NFractionalD.html