NCaputoD

NCaputoD[f,{x,α},x0]

gives a numerical approximation to the Caputo fractional derivative of order α of the function f at the point x0.

Details and Options

Examples

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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:

Numerical Caputo fractional integral:

Scope  (8)

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:

Plot this function:

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:

Applications  (3)

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:

Plot this fractional derivative:

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.

Text

Wolfram Research (2022), NCaputoD, Wolfram Language function, https://reference.wolfram.com/language/ref/NCaputoD.html.

CMS

Wolfram Language. 2022. "NCaputoD." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NCaputoD.html.

APA

Wolfram Language. (2022). NCaputoD. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NCaputoD.html

BibTeX

@misc{reference.wolfram_2022_ncaputod, author="Wolfram Research", title="{NCaputoD}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/NCaputoD.html}", note=[Accessed: 04-February-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_ncaputod, organization={Wolfram Research}, title={NCaputoD}, year={2022}, url={https://reference.wolfram.com/language/ref/NCaputoD.html}, note=[Accessed: 04-February-2023 ]}