Convoluted Fractional Poisson Process

In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking discrete convolution with respect to space variable in system differential equations that governs its state probabilities. We call introduced as (CFPP). The explicit expression for Laplace transform probabilities are obtained whose inversion yields one-dimensional distribution. Some statistical properties such probability generating function, moment moments etc. obtained. A special case CFPP, namely, (CPP) is studied time-changed subordination relationships CFPP discussed. It shown CPP L\'evy using which long-range dependence property established. Moreover, show increments exhibits short-range property.