Application of Fractional Derivatives in Characterization of ECG graphs of Right Ventricular Hypertrophy Patients

TL;DR

This paper employs Jumarie fractional derivatives to analyze ECG graphs, particularly focusing on right ventricular hypertrophy, demonstrating how fractional calculus can characterize unreachable points where classical derivatives fail.

Contribution

It introduces a novel application of Jumarie fractional derivatives and phase transition analysis to distinguish normal and problematic ECG signals, especially for right ventricular hypertrophy.

Findings

Fractional derivatives effectively characterize unreachable points in ECG graphs.

Phase transition differences help differentiate normal and hypertrophic ECGs.

Fractional calculus provides new insights into ECG analysis beyond classical methods.

Abstract

There are many functions which are continuous everywhere but non-differentiable at some or all points such functions are termed as unreachable functions. Graphs representing such unreachable functions are called unreachable graphs. For example, ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachable functions can be characterized by fractional calculus as fractional derivatives exist at those unreachable points where classical derivatives do not exist. Definition of fractional derivatives has been proposed by several mathematicians like Grunwald-Letinikov, Riemann-Liouville, Caputo, and Jumarie to develop the theory of fractional calculus. In this paper, we have used Jumarie type fractional derivative and consequently the phase transition (P.T.) which is the difference between left fractional derivative and right fractional derivatives to characterize those points. A comparative study has been done between normal ECG sample and problematic ECG sample (Right Ventricular Hypertrophy) by the help of the above mentioned mathematical tool.