gives a numerical approximation to the Caputo fractional derivative of order α of the function f at the point x0.
Details and Options
- NCaputoD is the numerical analog of CaputoD, also known as the Caputo differintegral of f.
- The Caputo fractional derivative of order of is defined as , where .
- NCaputoD is typically used in cases when symbolic evaluation with CaputoD fails.
- The following options can be given to NCaputoD:
AccuracyGoal Infinity digits of absolute accuracy sought PrecisionGoal Automatic digits of precision sought WorkingPrecision MachinePrecision the precision used in internal computations
Examplesopen allclose all
Basic Examples (4)
Calculate the half-order Caputo fractional derivative of a quadratic function with respect to x at a point:
Plot the -order Caputo fractional derivative of an exponential function:
Numerical Caputo fractional derivative of MittagLefflerE at some point:
Generate a list of numerical values of the Caputo fractional derivative of the MittagLefflerE function:
Plot this fractional derivative:
Plot the -order Caputo fractional derivative of the square function with respect to x:
Calculate the 0.23-order Caputo fractional derivative of the Exp function numerically and symbolically:
Calculate the value of the half-order Caputo derivative of the ArcTan function at some point:
The -order Caputo fractional derivative of the Sin function:
The -order Caputo fractional integral of the Sin function:
The half-order Caputo fractional derivative of the AiryAi function:
Numerically calculate the Caputo fractional derivative of the BesselJ function:
Plot the numerically calculated fractional derivatives and integrals of complex functions:
NCaputoD is able to numerically calculate fractional derivatives when CaputoD fails:
CaputoD outputs might be cumbersome:
However, the plot of numerically calculated fractional derivative might be insightful:
Effectively generate a list of numerical values of Caputo fractional derivatives of a complex function using NCaputoD:
The timing for the calculated 101 values:
Properties & Relations (4)
NCaputoD is defined for all real :
The Caputo fractional derivative of a constant is 0:
Plot the Caputo fractional derivative using the numerical NCaputoD approach:
Compare with the symbolic CaputoD approach:
For negative orders , NCaputoD coincides with NFractionalD:
Possible Issues (2)
NCaputoD will generate an error message if the precision of input is less than the WorkingPrecision:
NCaputoD takes only numeric points of evaluation:
Neat Examples (1)
Plot the Sin function and its half, first and -order derivatives:
Wolfram Research (2022), NCaputoD, Wolfram Language function, https://reference.wolfram.com/language/ref/NCaputoD.html.
Wolfram Language. 2022. "NCaputoD." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NCaputoD.html.
Wolfram Language. (2022). NCaputoD. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NCaputoD.html