Tempered fractional Poisson processes and fractional equations with <i>Z</i>-transform
Neha Gupta, Arun Kumar, Nikolai Leonenko
Abstract
In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes. We also introduce Gegenbauer type fractional differential equations and their solutions using z-transform. Our results generalize and complement the results available on fractional Poisson processes in several directions.
Topics & Concepts
MathematicsPoisson distributionFractional calculusCompound Poisson processComplement (music)Type (biology)Mathematical analysisApplied mathematicsSpace (punctuation)Poisson processStatisticsBiochemistryBiologyChemistryEcologyLinguisticsGenePhenotypeComplementationPhilosophyFractional Differential Equations SolutionsMathematical functions and polynomialsAcoustic Wave Phenomena Research