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seen Jul 2 at 14:44

Dec
15
awarded  Teacher
Sep
24
comment Howto plot a specific complex function
Done, thanks. .
Sep
24
awarded  Scholar
Sep
24
accepted Howto plot a specific complex function
Sep
17
comment Howto plot a specific complex function
Thank you Loïc for the suggestion! We will make an attempt to user your proposed method.
Sep
16
comment Howto plot a specific complex function
Thanks for your input Carlo! Solving it numerically is fully acceptable for us also, and this is what we have tried however without full success so far. I think the problem that we have not been able to circument in our naïve approach using the "fminsearch" Matlab function to numerically solve (1) is that both $\alpha(\omega)$ and $\beta(\omega)$ need to be positive. In addition, taking the power $a+1$ of the complex variable $k$ (that is $k^{a+1}$), is a multi-valued operation. Maybe you have some specific hint regarding ready-built methods to solve such constrained numerical minimalizations?
Sep
16
revised Howto plot a specific complex function
Small cleanups
Sep
16
revised Howto plot a specific complex function
I now just explicitly show in (1) that $k$ is a function of $\omega$, by writing $k(\omega)$.
Sep
16
asked Howto plot a specific complex function
Feb
7
comment The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Robert, your hint pointed me towards what I was looking for: the "generalized sine and cosine functions." More infor can be retreived e.g. from here: dlmf.nist.gov/8.21
Jan
26
comment Eigenfunction of local fractional derivative
From my point of view, your definition is strange, or at least it has a contra-intuitive feature: because $x$ and $\delta$ should have the same unit (e.g. some length unit), $\delta^\alpha$ will have the unit e.g. length$^\alpha$. Then $\tilde D^a f(a)$ will have the unit "meter$^{1-\alpha}$". But maybe this is OK? Please correct me if I'm wrong.
Jan
26
awarded  Editor
Jan
26
revised The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Correcting typos
Jan
26
comment The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Thanks a lot Robert for the hint. I will explore this further after the week-end. I even suspect that the Lommel S1 function might possibly be written in terms of the Incomplete Gamma function, but this I need to look up in detail. Again thank you.
Jan
25
comment Local fractional derivative that doesn't vanish on differentiable functions
I'm not sure, but maybe you could investigate the Yang local fractional derivative?
Jan
25
answered Are there analogous theorems and/or techniques for solving fractional differential equations involving the Riesz Derivative?
Jan
25
asked The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary