# Saigo Space-Time Fractional Poisson Process via Adomian Decomposition Method

## TL;DR

This paper introduces a new fractional Poisson process using the Caputo Saigo operator and derives its state probabilities with the Adomian decomposition method, simplifying the analysis compared to traditional Laplace transform techniques.

## Contribution

It presents a novel space-time fractional Poisson process based on the Caputo Saigo operator and applies ADM for deriving its state probabilities, offering a simpler alternative to existing methods.

## Key findings

- Derived state probabilities for fractional Poisson processes
- Introduced a generalized space-time fractional Poisson process
- Simplified the computation method using ADM

## Abstract

We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM). Generally these state probabilities are obtained by evaluating probability generating function using Laplace transform. A generalization of the space and time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.