In recent years, there has been a fast growth in the application of long-memory processes to underlying assets including stock, volatility index, exchange rate, etc. The fractional Brownian motion is the most popular of the long-memory processes and was introduced by Kolmogorov in 1940 and later...

The stochastic solution to diffusion equations with polynomial coefficients is called a Pearson diffusion. If the time derivative is replaced by a distributed order fractional derivative, the stochastic solution is called a distributed order fractional Pearson diffusion. This paper develops a...

We introduce a new distribution useful for positively skewed dataset with heavy tails and refer to it as the “Wright distribution”. Properties involving moments, skewness and kurtosis are studied. Simulation study and derivation of the density function using fractional calculus method are...