Alternative Forms of Compound Fractional Poisson Processes

Table 1

Main results in finite domain.

Process		Equation
CPP	𝑌(𝑡)	𝜉𝜕𝜕𝜕𝑡=−𝜆+𝜕𝜕𝑡𝜕𝑦
TFCPP	𝑌𝛽(𝑡)=^𝑑𝑌(ℒ𝛽(𝑡))	𝜉𝜕^𝛽𝜕𝑡^𝛽𝜕=−𝜆+^𝛽𝜕𝑡^𝛽𝜕𝜕𝑦
SFCPP	𝑌^(𝛼)(𝑡)=^𝑑𝒮𝛼(𝑌(𝑡))	𝜉𝜕𝜕𝜕𝑡=−𝜆+𝜕𝜕𝑡𝜕𝑦^𝛼𝛼
STFCPP	𝑌𝛽^(𝛼)(𝑡)=^𝑑𝒮𝛼(𝑌𝛽(𝑡))	𝜉𝜕^𝛽𝜕𝑡^𝛽𝜕=−𝜆+^𝛽𝜕𝑡^𝛽𝜕^𝛼𝜕𝑦^𝛼
ΔFCPP	𝑌Δ(𝑡)=^𝑑𝑌(𝒜𝛾(𝑡))	𝜉𝐷^1/𝛾−,𝑡=𝜆−𝐷^1/𝛾−,𝑡𝜕𝜕𝑦