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 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