FRACTIONAL DERIVATIVE OF THE POLYNOMIALS IN THE SPACE OF FOUR-DIMENSIONAL NUMBERS
DOI:
https://doi.org/10.63666/ejsmr.1694-9013.4.I.2026.109Keywords:
Four-dimensional space, power series, convergence, radius of convergenceAbstract
We explore the use of power series in solving generic polynomial differential equations in four-dimensional space, employing the Caputo fractional derivative. As is widely recognized, power series transform a continuous formulation into a discrete system of difference equations, which can be efficiently solved through recursive methods. The key contribution of this work lies in rigorously proving the convergence of these series in a neighborhood of the initial point. The theory of four-dimensional functions is the new method in mathematics and due to this is scantily explored.
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