Financial mathematics with new conformable derivative

Abstract

The significant features of conformable integrals and derivatives have been newly introduced \cite{2,3,4}. This study delves into the emerging field of fractional calculus, focusing on various definitions and distinct fractional derivatives. Notably, we explore the concept of "new conformable fractional derivatives" as introduced in \cite{1}.

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$\left(\mathcal{D}^\alpha F\right)(t)=\lim _{l \longrightarrow 0} \frac{F\left(t+l e^{(\alpha-1) t}\right)-F(t)}{l},$
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where $\alpha \in(0,1]$, its origin, characteristics, comparison with others
conformable fractional derivatives and its applications to financial mathematics ( construction the new fractional Black-Scholes option pricing model) .