Preprint Article Version 1 This version is not peer-reviewed

# Fractional Partial Differential Equations associated with L$\hat{e}$vy Stable Process

Version 1 : Received: 27 February 2020 / Approved: 28 February 2020 / Online: 28 February 2020 (13:09:14 CET)

A peer-reviewed article of this Preprint also exists.

Aljedhi, R.A.; Kılıçman, A. Fractional Partial Differential Equations Associated with Le^vy Stable Process. Mathematics 2020, 8, 508. Aljedhi, R.A.; Kılıçman, A. Fractional Partial Differential Equations Associated with Le^vy Stable Process. Mathematics 2020, 8, 508.

Journal reference: Mathematics 2020, 8, 508
DOI: 10.3390/math8040508

## Abstract

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

## Subject Areas

Price impact; Option pricing; liquidity, L$\hat{e}$vy process, fractional differential equations