5 papers
From a Student's Question to the Half-Derivative: A Constructivist Teaching Model - Part I
Davit Kapanadze
This paper presents a conceptual, cognitive-constructivist model for teaching the half-derivative. The model starts from a student's question and frames it as the problem of genera…
From the Half-Order Recurrence to General Fractional-Order Differentiation on Monomials: Functional Continuation and Operator Composition
Davit Kapanadze
This work develops a general-order fractional differentiation operator on monomials from the discrete half-order coefficient structure established in Part I. Starting from the one-…
An Algebraic-Operator Construction of the Half-Derivative on a Graded Monomial Space. Part I: Recurrence, Double Factorials, the Wallis Product, and Normalization
Davit Kapanadze
This paper constructs a half-order differentiation operator on the graded monomial space spanned by non-negative integer and half-integer powers of x, with x > 0. The algebraic sta…
A Limit-Free Algebraic-Geometric Construction of Derivatives for Elementary Functions
Davit Kapanadze
This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed fra…
A Limit-Free Algebraic-Geometric Construction of the Derivative with a Foundational Model in the Class of Polynomial Functions
Davit Kapanadze
This paper presents an algebraic-geometric construction of the derivative developed initially within the class of polynomial functions without introducing limits at the initial sta…