Fractional virus epidemic model on financial networks

Abstract

Abstract:In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

Innovative Interpolating Polynomial Approach to Fractional Integral Inequalities and Real-World Implementations

“…The findings we present in the following section extend the current body of knowledge and serve as a source of inspiration for researchers engaged in the study of mathematical inequalities. Finally, we refer the reader to learn about fractional calculus and its applications from the articles [35][36][37][38][39][40][41] and from the books [42,43]. The convex functions and related inequalities can also be studied in [44][45][46][47][48][49][50][51][52][53].…”

Fractional Interaction of Financial Agents in a Stock Market Network

“…Pearson correlation coefficient varies between -1 and 1. ρ i j = 1 indicates that the stocks i and j are completely correlated whilst ρ i j indicates that the stocks i and j are completely uncorrelated [42]. Hence, it is also possible to introduce a new distance d Corr := 2(1 − ρ i j )/2 as in [13,44]. We can conclude that if d Corr (i, j) = 0, then the stocks i and j are completely correlated, and if d Corr (i, j) = 1, then the stocks i and j are completely uncorrelated.…”

“…The threshold value can be determined by the subdivision of the interval [0, 1], where the boundaries are the extremal values of d Corr , into h many subintervals. The details on the algorithm of network construction and computational complexities can be found in [13,44].…”

“…In the complex network model of financial agents the interactions are modelled by the correlations of long time series [13][14][15][16][17][18][19]. Beside the other types of complex systems, financial systems have the strong memory and heredity properties.…”

Geometric Soft Sets

“…Since global stock markets are continuously in complex interaction they form a complex system and have long been studied by several researchers [4,12,23].…”