European option pricing models described by fractional operators with classical and generalized Mittag-Leffler kernels

In this paper, we investigate novel solutions of fractional-order option pricing models and their fundamental mathematical analyses. The main novelties of the paper are the analysis of the existence and uniqueness of European-type option pricing models providing to give fundamental solutions to them and a discussion of the related analyses by considering both the classical and generalized Mittag-Leffler kernels. In recent years, the generalizations of classical fractional operators have been attracting researchers' interest globally and they also have been needed to describe the dynamics of complex phenomena. In order to carry out the mentioned analyses, we take the Laplace transforms of either classical or generalized fractional operators into account. Moreover, we evaluate the option prices by giving the models' fractional versions and presenting their series solutions. Additionally, we make the error analysis to determine the efficiency and accuracy of the suggested method. As per the results obtained in the paper, it can be seen that the suggested generalized operators and the method constructed with these operators have a high impact on obtaining the numerical solutions to the option pricing problems of fractional order. This paper also points out a good initiative and tool for those who want to take these types of options into account either individually or institutionally.