Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov

Abstract

– In this paper, it has been proven that it would be more accurate to accept Euler, Riemann-Liouville, Caputo, and Grünwald-Letnikov methods as curve fitting or amplitude shifting methods without derivative definition. Since these derivative methods do not cause to shift extremum points of corresponding relations/functions to zero (the roots of relations/functions which are derived by taking fractional order derivative such as Euler, Riemann-Liouville, Caputo, and Grünwald-Letnikov methods).