Geometric algebra and (standard) calculus, when synthesized, give rise to geometric calculus, a very powerful formalism.
I have read a bit about fractional calculus and time-scale calculus, both very useful and promising for engineering.
I even found a paper about fractional calculus and time-scale calculus combined into a single thing called "fractional calculus on arbitrary time-scales".
I have not found, though, a synthesis of geometric algebra and fractional calculus analogous to the synthesis of geometric algebra and (standard) calculus in geometric calculus.
Similarly, I have not found a combination of geometric algebra and time-scale calculus.
Nor did I find a unification of geometric algebra and "fractional calculus on arbitrary time-scales".
I imagine such formalisms would be invaluable for engineering.
What are the names of such fields? What are their standard textbooks?
P.S.: I am particularly interested in developing an open source computer algebra system based on the most general formalism, because it should model hybrid models aptly and easily go from continuous to discontinuous (possibly covering the finite elements method).
Disclaimer: This question has been asked in mathematics and physics stack exchange (https://math.stackexchange.com/q/4967608/). There were no answers, despite views and comments. Therefore, I ventured posting here, even though I am not a mathematician.