Textbook recommendations, please

I'm currently investigating an idea I've had, and in that context I need to familiarize myself with both local and non-local Fα-calculus ("fractal calculus") on fractal sets. I don't wish to go into the details of the project just yet, as right now it only exists in form of a very rough outline, and I need to to investigate first if it is in fact worthwhile pursuing at all (chances are it might not be). Suffice to say I need a mathematical toolset that generalizes ordinary multivariate calculus / differential geometry on smooth differentiable manifolds to fractal sets with non-integer Hausdorff dimensionality. So I'm looking for a text that introduces Fα calculus, including fractal derivatives and integrals, both of integer and fractional order (think Riemann-Liouville with fractal measure); a generalization of the usual differential operators (div, grad, curl,...) to fractal sets; differential equations on fractal sets; and ideally Dirichlet forms.

I've got access to "Fractal Calculus and Its Applications" by Golmankhaneh, but I find it to be too technical for me as an interested amateur. I'm hoping perhaps someone here can recommend a text on the subject that is more accessible and builds intuition, rather than just listing definitions and lemmas? I've tried searching the Interwebz of course, but there appears to be surprisingly little literature on this particular subject - or perhaps I just didn't search for it right.

Thanks in advance!

Edited 5 hours ago5 hr by Markus Hanke

Hi Markus, I'm just going out so very quickly this might be a start for you

Chaos and Non Linear Dynamics

page 448 ff

Scaling and f(alpha) indices

Robert C Hilborn

Oxford University Press.

Sternberg has some stuff in his Dynamical systems book but I think you mqay have to find pieces of information in lots of different palces.

(Non linear) Dynamics is a key phrase.

I have some more to check so will post again later.

Let us know how you get on.

I cannot make any recommendations as the field, and literature, are mostly beyond my level, but you've made me curious.

Is this, in any way, related to the non-linearity of the EFEs, and the fact that they are extremely difficult to solve, usually employing linear approximations, which restrict their validity to a limited range of input values, and omit some other interesting results ?