Absolutely Fractional Differentiable Functions: Results, Examples and Counterexamples

Abstract

Authors have defined absolutely fractional differentiable functions on a closed bounded interval {\scriptsize $[a,b]$} of {\scriptsize $\R$}. Some significant results and equivalent conditions for the function to be absolutely fractional differentiable on a closed bounded interval {\scriptsize $[a,b]$} have been discussed. Several examples of absolutely fractional differentiable functions have been constructed. Counterexamples have also been constructed for some results.

Keywords: absolutely continuous functions, Caputo fractional derivatives, absolutely fractional differentiable functions