Questions tagged [fractional-calculus]
For questions about fractional calculus. Fractional calculus is a field of mathematics that deals with the generalization of differential and integral operations to an arbitrary order.
9 questions
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How is the fractional tanh plotted? [closed]
Suppose that the fractional tanh is defined as :
where E is Mittag Leffler function.
How we can plot tanh to get a graph similar to the following one:
I run this code and get this graph.
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How does Mathematica calculate a fractional derivative?
The Riemann-Liouville fractional derivative of order $1/2$ of $x^{-1}$ is defined as
$$
\mathcal{D}_x^{1/2} x^{-1} = \frac{1}{\Gamma(1/2)} \frac{d\;}{dx} \left[\int_0^x (x-\tau)^{-1/2}\tau^{-1} \,d\...
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Adapt Code to Solve Fractional-Order System Delay Differential Equations- Chen System
Dynamics of fractional-ordered Chen system with delay
I have tried to modify this code
...
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Riesz fractional derivatives/Laplacian for Lévy flights?
There are pretty popular Lévy flights for diffusion with steps of infinite variance, mathematically requiring Riesz fractional derivatives, which in Fourier transform multiplies by $|k|^\alpha$.
I ...
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1
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Find the derivative of the Caputo fractional derivative
I tried:
D[CaputoD[y[t], {t, 1/2}], t](* ? *)
(* 0 *)
And:
Integrate[CaputoD[y[t], {t, 1/2}], t]
(* 0 *)
I tried with ...
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2
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Fractional derivatives (FractionalD) of an InterpolatingFunction to retun another InterpolatingFunction
Question
I want to calculate the FractionalD of an InterpolatingFunction object, however, evaluating
...
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Fractional Differential Equation
I am facing the following problem.
If u[x_,t_]=t+y[t]x,
Then,
D[u[x,t],t]
Gives us
1+xy'[t].
But if I use the command for Fractional Derivative like
FractionalD [u[x,t],{t,a}], then Mathematica print ...
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2
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Integrating the sum gives different answer that summing the integrals of the terms
I wrote this code:
...
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