2017/11/07 by Srijan Sengupta, Sengupta, Srijan, Uttam Ghosh +5
Mathematics · Engineering · #Fractional Differential Equations Solutions #Advanced Control Systems Design
paper · pdf · doi:10.48550/arxiv.1711.02332
There are many functions which are continuous everywhere but\nnon-differentiable at some or all points such functions are termed as\nunreachable functions. Graphs representing such unreachable functions are\ncalled unreachable graphs. For example, ECG is such an unreachable graph.\nClassical calculus fails in their characterization as derivatives do not exist\nat the unreachable points. Such unreachable functions can be characterized by\nfractional calculus as fractional derivatives exist at those unreachable points\nwhere classical derivatives do not exist. Definition of fractional derivatives\nhas been proposed by several mathematicians like Grunwald-Letinikov,\nRiemann-Liouville, Caputo, and Jumarie to develop the theory of fractional\ncalculus. In this paper, we have used Jumarie type fractional derivative and\nconsequently the phase transition (P.T.) which is the difference between left\nfractional derivative and right fractional derivatives to characterize those\npoints. A comparative study has been done between normal ECG sample and\nproblematic ECG sample (Right Ventricular Hypertrophy) by the help of the above\nmentioned mathematical tool.\n