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:

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:

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:

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:

NCaputoD will generate an error message if the precision of input is less than the WorkingPrecision:

NCaputoD takes only numeric points of evaluation:

Plot the Sin function and its half, first and -order derivatives: