Progress in Fractional Differentiation & Applications

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In mathematics, the Riemann-Stieltjes integral 􏰝 f(t)dg(t) is known to be the more general version of the well-known Riemann integral that is used in classical integral calculus. This integral has found application in several fields. However, there is no clear derivative associate to the generalized integral, except the concept of global derivative that was suggested very recently. Nevertheless, a more generalized differential operator called conformable derivative was suggested and many concerns have been raised as what such operator cannot be considered as derivative. In this paper, we proved that not only the operator is a derivative but a derivative associate to the well-known Riemann-Stieltjes integral. We have in addition present some applications of the conformable derivative in image processing and dynamical processes including chaos and epidemiology.

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